Students at medical schools without an independent or integrated plastic surgery residency program (e.g. Downstate) will have a harder time matching into a plastic surgery residency program, because:
1) Fewer research opportunities. US seniors matching into plastic surgery had a mean of 14.2 publications/presentations/abstracts listed on their application. Plastic surgery is a very academic specialty, and the ability to work with residents on research projects is a massive advantage.
2) Fewer faculty. I've been told plastic surgery is a rather small field, and as a result, the names of your letter writers matters a lot. The existing faculty at these schools seem to be volunteer faculty who primarily work in cosmetic private practice, as opposed to tenure-track associate or full professors of surgery who do research on reconstructive procedures. Downstate's plastic surgery website lists a mere 3 faculty members, one of whom seems to have moved to San Francisco when I looked him up.
3) Lack of a home program to "fall back" to. I've heard that programs have a tendency to "choose their own," and without a home program, you'd be more reliant on sub-Is and audition rotations at other institutions to impress program directors.