The title pretty much sums up the question. I don't have any of the books but I specifically want the rules as they might apply to a fantasy setting and players (not sure if there are any rules that are specific to players vs. NPCs). Preferably the rules would allow for at-will flying. I would assume that it would be an Edge (or multiple edges) but I'm not sure.
Savage Worlds has flying rules. They are usually summed up in a sentence or two as part of the ability or race that gives flight. For example, the Avion example race has wings, and its ability to fly is covered by two short sentences of rules. They're covered more generally in all of one paragraph in the Monstrous Abilities section of Savage Worlds Deluxe (p. 131), but that's just to save a sentence for each monster. Flight rules are a very straightforward extension of the normal movement rules – it's very easy to handle flying characters.
To be able to fly, you can use the Fly Power (p. 113), either by being a spellcaster or finding a magic item with the Power. Alternatively, you can just have wings, which in a fantasy setting can be acquired in any number of plot ways given GM cooperation.
In the race-construction rules (p. 22), being able to fly is roughly equivalent to an extra Novice Edge, so if you want to make an Edge called "Wings", that's totally doable. Give it requirements that make it sensible (instead of "Hey Bob, I just levelled up and look! even though I'm a normal human I grew this gorgeous pair of wings!"), and you're good to go.