I'll still hold with Fleming on this one: the old story of Anglo-Saxon conquest is overblown, and a much more fluid story of assimilation and innovation seems likely. These points, although certainly worth considering, do not in themselves support the theory of massive migrations. That is to say, if you start with the story of a massive Anglo-Saxon migration in mind, these points certainly support that story, but if you had just these points and nothing more, it would difficult to deduce the conquest story that previously dominated our understanding of post-Roman Britain.

1. Genetics. Fleming doesn't discuss DNA much (if at all) because that's outside the purview of the book project; she states in the introduction that she wanted to avoid getting into debates with scholars that would distract from the story she was trying to tell. And at this point, I think that's what DNA evidence tends to be: a distraction. It's completely undatable (okay, you could take DNA samples from early medieval cemeteries, but this is way too expensive and the data set remains far too small; the reviewer seems to overestimate the resources available to historians and archaeologists). Modern 'Germanic' genetic material could certainly be a relic of a massive Anglo-Saxon invasion. But it could also come from nomads crossing into Britain during the last Ice Age, Germanic mercenaries hired to serve in the Roman military, Frisian traders who populated later Anglo-Saxon trading towns, or mercenaries and administrators brought into England during 300 years of rule by the House of Hanover. It was probably a mix of all these things, which leaves us no way of assessing the actual genetic impact of the supposed Anglo-Saxon invasions.

2. Linguistics. This is also a difficult strand of evidence, since it rests on assumptions that people will always develop creole languages in situations of cultural assimilation. It's important to note that our best linguistic evidence for Old English dates from after 700. This was a period of consolidating kingdoms, and many of the Anglo-Saxon elite (notably including some of our favorite authors: Bede and Alfred the Great) were promoting a certain vision of Anglo-Saxon culture that would help them unite their diverse subjects. This is similar to how more modern governments suppressed regional identities in part by adopting national languages that effectively suppressed many regional dialects. In short, we have only good guesses about what Old English would have sounded like before the 600s, but we don't know how many dialects and creolized languages were lost before ever being written down. Linguistics can be very compelling evidence for very many things, but we simply lack sufficient information about spoken languages to argue that there was no creolization in the centuries between the dissipation of Roman rule and the rise of a new literary culture in Britain.

3. Literature. Gildas was a priest delivering a sermon and apparently circulating it among a Latin-literate Christian audience in Britain for whom we have no other evidence. In fact, Gildas is our only contemporary written evidence for Britain in the 5th and 6th centuries. So on the one hand he might tell us a lot about the arrival of an unknown number of war bands, painted in gruesome detail as the overwhelming forces of Satan, as befits the hyperbole of a sermon. But on the other hand he also tells us that he thought Latin literary culture would continue in England, and that Gildas actually anticipated continuities rather than conquest. Add to this the fact that many modern readings of Gildas (who has some strange and tricky bits of Latin) have been influenced by Bede's interpretation of Gildas, and recent studies suggest that Bede made many assumptions when he incorporated information from Gildas into his own Ecclesiastical History, and that some of his assumptions may very well have been mistaken.

4. History. These arguments fail to satisfy. Why couldn't Saxon pirates during the Roman period have grandchildren who were more interested in farming during the post-Roman period? Indeed, with the complete collapse of the British economy in the 5th century, there was little incentive to go a-pirating in Britain. Without the surpluses of the Roman economy to leach from, even Saxon pirates would have needed to turn to farming to feed themselves. And the Saxon-Celtic dialogue that the reviewer supposes is likewise absurd. People who immigrated from the Continent most likely (a) integrated with old military communities with whom they already had cultural ties through generations of mercenary immigration, or (b) took over the less productive lands in looser soils, which had been largely neglected during the Roman period in favor of intensive farming in heavier dirt. In the long run, these less productive but less intensive farms might actually have been advantageous, since they took a little less time, allowing the farmers to pursue all the other needs of subsistence that hadn't been necessary back when Roman markets made leather, nails, textiles, and a host of other items more readily accessible to the general population.

5. Demographics. I'm not sure why this is an assumption. Settlement patterns dramatically changed in the 5th and 6th centuries, so it's probably better to conceive of this period more as a shuffle, as some new Anglo-Saxon cards were added to the deck and just so happened to come out on top.

To be fair, I don't think we'll ever have the definitive answer about what happened in this period, although I think we're starting to ask better questions about it, and ditching the old story of Anglo-Saxon conquest has really helped us understand the evidence we have much better. If you enjoyed Fleming's Britain after Rome, I'd strongly recommend Halsall's World's of Arthur (2013). He gives a really good review of where the Anglo-Saxon conquest came from and why it seemed so compelling to many scholars, and then he offers his own theories for what actually happened after Roman rule in Britain. I think Halsall's views are very compelling and largely consistent with Fleming's, although his very different focus and emphasis provide a useful alternative perspective.

These are fantastic questions. /u/textandtrowel's response is excellent, and I would agree with most of what they say, but I also have a different enough perspective to warrant a longer response of my own. Let me jump straight in with my thoughts:

Genetics

First, genetic studies. We should begin by recognizing what it means to say that someone has 'Germanic' or 'Celtic' DNA. Despite the claims of modern white supremacists, the genetic differences between European populations are incredibly subtle. Two recent studies (one and two), both published in Nature, sought to identify genetic clusters in Britain and neighboring parts of Europe, and in all cases the differences they found were restricted to subtle mutations whose geographic patterning was statistically significant.

We should be aware of a few cautions with this type of data. First, there's a risk of p-hacking, that is of mining a dataset for some kind of pattern that's statistically significant until one is found, and then assigning that pattern a lot of analytical weight. This is an extremely common problem in scientific studies that has been receiving a lot of critical attention in the past couple of years: you can always find some sort of pattern if you look hard enough, but you risk confirmation bias if your experiment isn't very carefully designed. Recent DNA studies of Britain vary in quality, and the results they've found are in some cases very subtle, and have been blown entirely out of proportion by the press. One article, for example, argued that Britain was still tribal because the study proved its population was divided into separate genetic lines - in fact, the study found the opposite! Everyone in Britain is related, and the differences that could be measured were incredibly subtle.

The second issue is that these studies depend heavily on models which are still very new and poorly tested. /u/textandtrowel covered this well, when they said that it's very difficult to identify precisely when these subtle genetic mutations originated. Studies which find significant 'Anglo-Saxon' DNA (like the one you cited, or the first Nature study) assume that the similarities they find between Germany and England resulted from the Anglo-Saxon invasion because Bede says that's when a lot of people crossed the North Sea. Most of these studies are equally consistent with a model of longer-term, gradual migration. And in fact, we have good reason to believe that people have been migrating across the North Sea with some frequency for the past 6000 years. This doesn't mean that there may not have been a spike in migration in the fifth century; but the scale of migration needed to produce the patterns found in modern DNA is different if we assume a single event vs. a longer term process. Ie, there are a lot of questions that aren't yet well answered, which is why the two most recent DNA studies found that 6th century Britain's population was anywhere between 10-40% immigrant (the first study), and 25-50% (the second). These numbers, if correct, are not insignificant; but they're also not at all consistent with the old narrative in which invaders drive the local population off the landscape and replace it. A 10% (or even 40%) migration means that the majority of the population was always descended from local Romano-British.

The second of the studies to which I've been referring studied ancient DNA from several skeletons. The poor preservation of the bones, coupled with limitations in funding, meant that they were only able to study a handful of skeletons, but they concluded that the single cemetery (Oakington) from which the majority came contained immigrants from the Continent, locals whose genetics were consistent with Iron Age British populations, and children whose ancestry was mixed. This entirely supports Fleming's argument for accomodation and intermarriage. The study also found two 7th century first-generation migrants from the Continent, which confirms - in an anecdotally small sample - that migration was an ongoing process, not a single event restricted to the fifth century 'invasion'.

There's a new project underway which is trying to do precisely what you propose: study bodies of men with weapons and men without from the same cemetery, and see what their genetic stories are. I have mixed feelings about this study. On the one hand, a few bodies from a single cemetery is a small enough sample that it can't do much beyond confirm the biases of whichever 'side' is vindicated by the results: one cemetery where locals have weapons and migrants don't won't convince die-hard adherents of the old invasion story to change their tune, and a single case that confirms the old narrative won't overturn the growing body of material evidence that refutes it. More fundamentally, the study risks confusing ancestry with culture: a person born in Germany could be culturally 'British' / Celtic, and a local might adopt an 'Anglo-Saxon' identity. Ethnicity is cultural and mutable, and we risk falling back into 19th century scientific racism if we pin all our hopes on someone's blood to tell us who they were in life. But I'm glad that this question is being investigated, as more data is always a good thing.

What's the tl;dr of all that? Genetic studies are fascinating, but they're also new and their full potential is only just starting to be explored. We tend to give them more weight than, perhaps, we ought. That said, they seem to generally confirm the growing consensus that migration in the sixth century was smaller than the old invasion story assumed, that migration was a longer process than a single invasion (lasting centuries, perhaps even millennia), and that populations intermarried and co-existed. I personally think they confirm rather than challenge the views of Fleming (which reflect a growing consensus among Anglo-Saxon archaeologists and historians).

(cont)