Does physicalism think a priori knowledge exists? If so, how is this knowledge explained? Is the idea like morality being coded in DNA?
For any rational physicalist, evolution by natural selection is the the most likely method by which our brains evolved. Evolution is a process whereby biological forms and behaviours which less effectively exploit niches in competition with other more efficient forms and behaviours produce fewer and fewer copies until eventually none are left. It therefore follows that any behaviour encoded in our DNA would constitute "knowledge" of a successful method for survival in the niche in which the behaviour evolved, so technically this would qualify as a priori knowledge.
There are also schools of thought such as Ian Stewart's concept of morphological form, which use the limits of the physical world on biology to constitute a kind of "knowledge" of what can and cannot exist. Because our brains evolved within limitations such as linear time, three-dimensional space and gravity, such truths are hard-wired into our brains. Of course, in this case they are pragmatic "truths", not actual truths as science has proven all of them to be other than that which we intuitively believe them to be. If, however, you accept definitions of knowledge such a those of Pierce, then this kind of hard-wiring would also constitute a priori knowledge for a physicalist.
The important question really for physicalists, is not whether such knowledge exists, but how to identify it as such, and how useful or applicable it is outside of the specific niche in which it evolved.