Too bad someone with limited knowledge on this topic is giving you advice, but I thought I should let you know anyways.
No, your explanation was quite useful. The fact that you got your game runnign using AIR is evidence enough that AIR is a viable environment for running more robust Flixel games.
The primary challenge that I see is adapting Flixel to load external files for graphics, music, etc... Flixel is built around embedding assets, but one of the advantages of building an AIR application would be installing the game to your hard drive and using local assets. Fortunately, I've already created a solution for loading external graphic resources into Flixel, so that also is possible. I might have to change up how Flixel handles the pre-loading, but that goes hand-in-hand with external asset loading.