Here you go:
http://www.fs.usda.gov/recarea/inyo/recreation/camping-cabins/recarea/?recid=20390&actid=29Looks like one night only there; a walk-in close to the parking lot. Be advised: get to the parking lot really early (by 7 AM) in the morning to be assured of a space.
There are other campgrounds just down Rock Creek road from M/Flat. Check the same website I listed above. Good luck.
You will love Mono Pass; a real moonscape, but beautiful views. On your return from Mono Pass, don't forget the Pie-in-the-Sky Café near Rock Creek Lake; pie to die for. Seriously.