You can.
ALT-R toggles the flight recorder on and of. When you are recording, you see a red "R" in the upper left corner of your screen.
All your recorded films are located in your Aces High game folder (the standard path is c:/programs/HTC/Aces High II/films). You can view these films by either going there and doubleclick on a film, or by starting your Aces High Film Viewer first, wich is a seperate program located at the same location as your game. In both instances you have to end game first, you can't watch your films while game is still running.