Snapedom

Leaning in favor towards the latter theory is the fact that Lily was able to fly as a child. Unaided flight is supposed to be impossible for wizards, so that would appear to be quite a remarkable feat, even if it was merely the sort of spontaneous wandless magic that young witches and wizards exhibit, that fades as they get older. At the time, Muggleborn Lily would not have realized that how remarkable this was, but Snape, having been raised by a witch mother, might have. I could see them having tried to develop a flying spell when they were older.

If they did begin researching such a spell while at Hogwarts, they probably weren't successful, since the spell doesn't seem to be common knowledge. Surely they wouldn't have been able to resist showing off such a spell, and we've never heard about anyone flying at Hogwarts during the Marauders era. Slughorn spoke effusively about what a talented Potions student Lily was--surely he would have mentioned if she had been able to do something as remarkable as flying without a broom. Surely Lily would have shared such a useful spell with her husband and maybe the other members of the Order.

So Snape and Lily probably didn't invent such a spell when they were teenagers. It is possible that they were able to make a few significant strides towards it, but were unable to perfect the spell before Lily severed their friendship. And afterwards, they abandoned their research and chose not to continue it singly, since it brought back too many painful memories.

However, it is possible that years later, while doing some unrelated research for either Dumbledore or Voldemort, Snape stumbled across something that helped him complete the flying spell. Then at some point, probably when he needed to curry favor with the Dark Lord, he gave the finished spell to Voldemort. Voldie doesn't seem like the type to give credit to others, so he doesn't broadcast that Snape is actually the one who invented the spell, and everyone assumes that he created it. Snape, playing the role of the loyal lackey, keeps quiet and lets Voldemort take the credit. (And even if the Death Eaters knew that Snape created the spell, Mcgonagall probably wouldn't have been privy to that information anyway.)

But...a big problem that I have with this scenario is that Snape regards his memories of Lily as something very painful and private and precious. Of course he wouldn't tell Voldemort about Lily's connection to the spell, but I can't see Snape sullying her memory by giving something that he associates with her to the Dark Lord. He would do it only as a last resort, if there was no other way to fulfill the promise that he'd made to Dumbledore, to protect Harry for Lily's sake.

And quite frankly, it seems like killing Dumbledore would be enough to win Voldemort's favor without needing to give him a flying spell, which is pretty cool but hardly vital to the Dark Lord's plans to take over the wizarding world and kill Harry.

I suppose that it's possible that Snape could have given the spell to Voldemort prior to Dumbledore's death, and that Voldie didn't have an opportunity to use it publicly until that scene in Book 7. Perhaps when Snape returned to the Death Eaters at the end of Book 4, Voldemort was extremely distrustful of him, and the spell helped win him a little goodwill. Still, it seems like a clever spy like Snape would be able to work his way back into Voldemort's trust without it, and if Voldemort was that mistrustful of Snape, I don't think that a nifty flying spell would be enough to ease his suspicions. Snape would have had to do something more direct to prove his loyalties: provide important information, and/or help take out some of his Order allies, as he claims to Bellatrix that he did in Book 6.

So perhaps Voldemort really did invent the flying spell (or rediscovered a long-forgotten spell), and gave it to Snape as a reward for killing Dumbledore. Or Snape was the one who created the spell and gave it to Voldemort, but it had nothing to do with Lily: it was something that he researched on his own, out of curiosity, or because he doesn't like using broomsticks. The Pensieve memory of him in Book 5 as a young boy on a bucking broomstick may be a hint that he isn't good at it, although he seems to have mastered the skill sufficiently enough as an adult to referee Quidditch games. Maybe the research into the flying spell originally started off as a way to compete with James: if Snape couldn't be a naturally talented broomstick rider like his rival, then he could have decided to one-up James and do something better--fly without a broomstick. But again, since he didn't show off the flying spell in school, he probably did not perfect it until years later, long after his rival was dead. By then it might have seemed pointless and a hollow victory, so he had no qualms about turning it over to Voldemort to gain some favor rather than keeping it for himself.

Or maybe it was something as simple and trivial as Voldemort expressing a whim for such a spell, and Snape set out to impress him by achieving the impossible. Or, as I suggested earlier, he came across the flying spell while doing research for something unrelated, and thought it might be useful.

Still, it does seem like a pretty big stretch of coincidence that Lily, Snape, and Voldemort are the only witches or wizards that we see who can fly without a broomstick, but I can't quite figure out how to connect the three in a way that makes sense.