We know for certain that khipu were used for something besides numbers. But that's about all we can say. We have two main sources on reading khipu: coloinal accounts and modern analysis.

For what it's worth, colonial-era writers did try to record what they could about khipu. Unfortunately, the bulk of their writing is broad and ethnographic, not the kind of quantitative descriptions a khipu "translator" would want. What we do know is that community members called khipukamayuq were able to consult khipu to extrace a variety of information. Cieza de Leon and Garcilaso de la Vega tell us they were used to record census and tribute data in the manner of an Inca IRS database. Guaman Poma claims they could store astronomical/calendrical information, and Cristobal de Molina writes about them recording historical narrative. Two chroniclers, de la Vega and Antonio de la Calancha, even claimed to have learned to read khipu.

Now the most useful thing that the Spanish let behind are, unsurprisingly, khipu transcriptions. These are records in Spanish, Latin script translating khipukamayuq speaking in Quechua or Aymara, reading from a khipu. Since they're mostly from interactions between the invading governing force and the wily local politicians who seized the opportunity of a new imperial force to grab some power for themselves, the transcriptions discuss those most exciting topics of censuses and tax reports. Yeah, we could wish for some of the more abstract ones, but these do in fact tell us a lot. There is a consistency of specific names for government offices, tribute items, locations, plants, animals, etc. that suggests they were directly coded into the strings. They are also arranged in regular patterns and formulas that, though not invariable, lends some semblance of "grammar."

These transcriptions are a boon to modern analysis. There's a lot working against it though. Provenience of most known khipu is awful, with many of them not even being veritably Inca: the khipu tradition dates back at least to the Wari empire of 600 AD. It's clear that there are sets of khipu that belong togehter, but we only have a handful of small, certain sets. Identifying these sets is incredibly useful. From a set of just 7 khipu frm Puruchuco, for instance, researchers were able to identify consecutive hierarchical reports. One pair of khipu summarizes the information on another known pair alongside other unknown data sets, in the same way a state census report would summarize/contain the data from various county reports. Khipu pairs have also been found with almost exactly the same information, suggesting two chronologically sequential records of the same type.

Of course, these are all numerical, quantitative khipu with a clear decimal system in use. The other, more abstract, "narrative" khipu remain a challenge in most regards. The jury's still out on whether they might be considered "writing." I, in my observation of the data, would not go so far as to call them writing, in that they do not represent a physical recording of spoken Quechua or Aymara. They have their own logic separate from patterns typically seen in languages.

If you're interested in khipu, take a look at anything by Gary Urton that you can find.