What is the process and timeline for someone to be chaptered out of the Army?

Thats is a lot like asking "How long will I wait in line at the Drivers license office."
The answer is...It depends.
When the priority is there at unit and higher HQ to separate a service member, it can be done in about 48 hours..... I did so for a SSG former Drill Sargent at FT Jackson.
In a unit that has other priorities, or some level of dysfunction...5,6,10 months is possible.
If the administrative process is being looked after by a competent person, the SM being separated is actively participating in his processing in a helpful manner vice dragging their feet (missed appointments, failure to bring required documents, failure to perform required briefing, sign forms, ect ) or attempting to stall or reverse the decision plus all key signatory persons are locally available 8-20 weeks is common.

If they aren't looking to send him to jail for a stint, you can expect your son to be chaptered out within the next two or three months. I personally walked soldiers through chapters and they can get finished in as little as a week.

They'll probably be out shortly into the new year. Just depends on where he is at.
Assuming he doesn't continue to screw up. Every time he goes AWOL, fails a UA, or isn't where he needs to be, new charges are added. New charges reduce his discharge rating and take away more benefits. Hopefully, he stops digging the hole he's in already.