I think this is an interesting question but things might be cloudier if we ask what is meant by knowledge in each case.
Yes, on the simplest reading, if JTB states all knowledge is justified true belief, then it would, as Derek suggests, seem to be incompatible with a claim that people can have innate knowledge.
But we need to ask if these two things do mean knowledge in the same way. JTB seems to be mostly talking about facts (Sache) or states of affairs. And it's a theory about when we "know" a state of affairs to be true. A relevant SEP article for instance points out that what is meant is "propositional knowledge."
Innate knowledge, in contrast, may or may not be about facts. Plato's version clearly seems to include something along these lines in that the true knowledge (which depending on the dialogue is either innate or inaccessible is the Forms). More often, in contemporary versions, it seems to be about structures or even a theory about how cognition works (i.e. Kant or perhaps implicit grammar). As such, the idea that there's some sort of "innate knowledge" or "a prior cognition" is not automatically incompatible with a JTB approach to fact claims.
Moreover, it seems difficult to design a form of JTB that by that means something completely expansive about "knowledge." For instance is knowing that JTB is true a JTB? Is recognizing that we apply cause to things in the world a JTB?
See also: If there is a difference between a priori knowledge and innate knowledge, what is it?