Yeah, I wouldn't push too hard for Flat Creek with so many other great options in the area.
It is about the closest to Jackson (Town Square) and easy to get on. I've only fished it in late Sept. - early Oct. and all the fish I've caught have been on small mayflies.
It's pretty cool.
When the hatches come off (from what I've seen) it's never a huge amount of bugs but there can be several different kinds going and they get pushed into the tight current seams against the bank.
Those huge cutties will sit super tight to the banks and casually sip away requiring a stealthy approach, fine tippets and very accurate casts with difficult drifts. They refuse and ignore poor matches to the hatch so you can easily sit there for 1/2 hour to an hour working one rising fish. It's quite the sense of accomplishment when you finally get one to take after changing flies three times and running 30-40 drifts by the fish without spooking it.. and then things get complicated. Those banks are deeply undercut.
Here's a quick video;
Fly Fishing Flat Creek | High Country Flies
The fish they show is actually on the small side from what I've seen and caught.
I've also never dealt with crowds but I don't doubt that it happens.
It's fun just hiking around looking for a riser, and you can almost always find some if the hatch is on. At least that's how it's been for me though I've only been on it maybe 10 times in the last ten years.