Always figured that everyone flies differently even if the result is the same. Superman's got some weird solar-powered alien organ that, under the yellow sun, converts energy and gravity into flight, Captain Marvel (Carol Danvers) was infused with alien energies (Kree and cosmic and probably more to boot) through an accident involving Captain Marvel (Mar-Vell) that she can now project to move herself through space, Captain Marvel (Billy Batson/Shazam) is straight-up magic, Captain Marvel/Photon (Monica Rambeau) is constantly shifting/transmuting molecules around her. And those are just the Captains Marvel I know.

As for Superman fic, you could go a lot worse than the silver age "Miracle Monday" story by Elliot S! Maggin (available here) though it's hard to say whether or not it's quite as good if you don't already love the guy.