Hanbali, just look on pubmed. You're a medical student - you should know how to do basic searches. You can also look at the proposed rotations for the programs you're considering.
Here's a list of VA-affiliated medical schools (so residency programs affiliated with those schools also will have VA time):
Affiliations List - Office of Academic Affiliations - U.S. Department of Veterans Affairs
You didn't answer my question - are you going to seek out non VA-affiliated programs or not do medicine if you don't get into one of those (very few) programs due to your beliefs about the armed forces?