Can Trump fire him?
Not sure, but I think congress, or the USAF Chief of Staff could look into it, unless he is an Obama general too. I am not sure, but I think someone is looking into that West Point communist too.
Now, I don't think the USAFA superintendent committed some horrible crime, like murder, but he certainly showed EXTREMELY poor judgement, and his career should be over, Force him to retire. It's possible he might be an Obama General, but I don't know that for sure, either.