Did he have a dishonorable discharge or a bad conduct discharge? I think it makes a difference. But the domestic abuse while he was in the Air Force should have prohibited him, I would think.
Several publications said that it was a bad conduct discharge and a year of confinement. Here’s one.
http://www.dailymail.co.uk/news/article-5053013/Devin-Kelley-outcast-preached-atheism.html