I would not bring it up directly.
PTSD in the military is a sign of weakness, which to me is totally ridiculous.
I convinced my uncle to go who is a Vietnam veteran. His pride was getting in the way, and he didn't want to admit that he had a problem. I started talking to him about the problems that i was having. If i were you, I would study up on the symptoms, then talk to him about "a friend of yours" that is having problems like hyper-vigilance, nightmares, and other PTSD symptoms. Then ask him what would he do.