First, he will have to demonstrate that there was an error of process, regulation or law. That is usually exceedingly difficult to prove.
Not sure about other Services, but our Discharge Review Board limits the petition submission window to 15 years. BCMR is three years from discovery.
So, why, exactly did he get an OTH. Did he request one in lieu of trial by court-martial? How long was he AWOL? We're pretty hard core, but I don't issue OTHs for anything other than egregious misconduct. Seems like there's more to the story than he's actually telling you.
Bottom line is that it's highly doubtful he'll be granted relief. He committed at least one act of misconduct, and he has learned the rather harsh lesson that adult behaviors beget adult consequences, sometimes lifelong consequences.
I separate around 1000 enlisted members from the Coast Guard each year.