Fat? Not really, but they look it thanks to their patagium. Fluffy? Oh fuck yes. Rodents? Yup!
Flying squirrels, of course, can’t really fly. They glide using the fluffy flap of skin between their fore- and hind legs as a parachute and those ridiculous squirrel-tails of theirs to steer and brake. They tend to be fairly small animals, with the largest species topping out at two feet. They also tend to have a fairly high mortality rate, because a) squirrels and b) juveniles of anything that flies have an unfortunate tendency to smash themselves into things.
Most species are nocturnal thanks to “squirrel in the air” being what eagles and hawks saying instead of “fish in a barrel.” Seriously, though, at least birds can properly fly if they find out a hawk is gunning for them. Squirrels in mid-air are just sitting there going “Get eaten, fall to my doom, get eaten, fall to my doom? Why are choices so haaaaaard?”. Not fun.
Fortunately for the squirrels, their ability to glide from tree to tree involves some ability to catch up-drafts where available and recorded flights of like 300 feet, so they do okay for themselves even in patchy habitat and under rough conditions. They can cover a lot more ground than a strictly arboreal squirrel, and natural barriers like rivers pose less of a problem.