This 'prophecy' is completely wrong in terms of its history, with even a cursory look at wikipedia being more than enough to disprove it. Though I am curious to know where you found it - reading terrible descriptions of Late Antiquity is my guilty pleasure :)

For a start, what did it mean by the Fall of the Roman Empire? I imagine it was talking about 476, when the Western Roman Empire technically ended, but that ignores that fact that the Eastern Roman Empire still ruled the Eastern Mediterranean and was as powerful as ever. In any case, many of these kingdoms were established well before 476, as the Vandals, Franks, Visigoths, Burgundians and Suevi were all settled in their respective regions for decades by then.

Nor would it be correct to say they were kingdoms, since just in Anglo-Saxon England, there were the kingdoms of Deira, Bernicia, Mercia, Wessex, Kent, Maegonsaete, Hwicce, East Anglia and more that I can't remember right now. And this is ignoring the British holdouts in England, such as in Dumnonia in modern day Cornwall. The same is true for the Franks, who were divided into the Salian and Ripuarian Franks (maybe more, not an expert on their early history I'm afraid), that only conquered what is now modern-day France under Clovis around 510-ish, a good four decades after the end of Roman rule in Gaul! Likewise for the Visigoths, as they were divided into a bajillion factions in the early fifth century, only being united by Leovigild in the 570s.

Lastly, what did it mean by 'rooted up'? There is a terrible way to describe the Vandals, Heruls and Ostrogoths, as their situations were all very different from each other. The Vandals had settled in Africa since the 410s and were in power until the 530s, the Heruls pretty much stayed in Pannonia as far as I know, whilst the Ostrogoths migrated to Italy in the 590s and has a much better claim to being a post-Roman kingdom than the Lombards, who only moved from the Balkans to Italy in the 560s.