What does the process of reenlistment look like for me if I got a Chapter 11 discharge (separation JGA, discharge type uncategorized)?

With a JGA I'm guessing you didn't do very well in basic....what's the story there? Because as a recruiter it's the first thing I'm going to ask if you call and I HIGHLY recommend not putting lipstick on the pig as a good recruiter will find documentation to back up or refute your narrative. It really depends on the situation and how you reacted to it. I have yet to read the rule on the Air side that limits anyone's time before they can reapply...that's just a tactic to get you moving along and out of their hair for a period of time typically.

Second chances are not easy to get so a whole-hearted effort is the only approach for sure.

If you wish to enlist it will be a waiver, only a recruiter can tell you exactly what you require. Chances are not good. Good luck.