He needs to make a simple statement and STOP:
Some folks are politicizing the character of my military service during the Vietnam conflict. As you know, I served in the Texas Air National Guard. I completed my service obligation satisfactorily as did many other Americans during this divisive era. I will not discuss the matter further. Instead I choose now to focus on America's future.
If you're in a hole, the first thing to do is stop digging.