As the comments already suggest, it's basically just in major. If you want to call it a mode, that would be Ionian, but it's pretty strongly based on dominant–tonic relationships, so I think "major" would be more accurate than "Ionian." (See What is the difference between C major and C Ionian?)
The opening is all based on the C-major collection, and it's a bit reminiscent of Terry Riley's "In C." Around 1:20, Conti introduces a couple of accidentals (among them B♭ and E♭), but this is really just a transition to what begins at 1:23, which is really D Dorian. But interestingly, this D Dorian includes the exact same pitches as C major. Thus he hasn't changed any pitches, only the tonal center. By about 1:45, he's already moving back to C major.
At 3:41, he moves to D major.
In short, this is all pretty standard tonal material. "That specific flying feel" is, in my opinion, due more to the instrumentation and motivic material than to any particular mode.