The Imperium utilizes four primary aircraft: the Lightning Fighter, Thunderbolt Heavy Fighter, Marauder Bomber, and the Valkyrie VTOL Troop Carrier. Within these four aircraft there are several modified for different roles: the Lightning 'Strike' fulfills a ground attacks role, along with the Marauder 'Destroyer'; the Valkyrie 'Vulture' gunship, 'Vendetta' heavy gunship, and 'Sky Talon' heavy lifter. There are also more civillian craft in the Arvus Lighter and Aquila Lander, but these largely lack combat capabilities.
Also of note are the aircaft of the Adeptus Astartes. The one-man Stormtalon gunship, the lightning-fast Stormraven, and the heavier Thunderhawk and Storm Eagle attack craft all have devastating firepower.
The enemies of Mankind are not without air power, though. The forces of Chaos utilize dark designs forged within the Eye of Terror, with Hell Blade Interceptors and Hell Talon Fighter-Bombers alongside more common Imperial vehicles. The crude Orks fill the skies with lead from a wide arsenal of ramshackle craft, with the Fighta-Bommer, Heavy Bommer, Dakkajet, and Warkopta among the most numerous. The Dark Eldar have one of the most fearsome selection of aircraft in the Spinward Front, packing cruel weaponry and impossible speed into light craft; the Razorwing and Raptor Fighters both have maneuverability that fills many Imperial aces with fear, while the Voidraven Bomber carries weapons of terror and mass destruction.
I think there's definitely something here. A party could easily be a few fighters escorting a bomber to its target, protecting a civilian craft with a VIP onboard, or scrambling to launch a counter-attack against an enemy strike. You could theoretically expand it into space (but I fear for stepping on Rogue Trader's toes) and have an incredible campaign in the vein of Rogue Squadron, with daring Fury and Starhwak pilots.
I have no idea about the Specializations for a squadron, though.