There is no cheat code in Grand Theft Auto III that makes cars fly. The game's physics engine (2001) doesn't support flight mechanics for ground vehicles.
On PC, mods like GTA III Admin Console, CLEO scripts, or vehicle handling mods can enable flight, but these require third-party tools and may break missions or stability.
GTA III focused on driving, shooting, and exploration—not physics simulation. True flying vehicles arrived in GTA: Vice City (helicopters) and GTA: San Andreas (planes, jetpack, flying car cheat). If you want flying mechanics, later GTA titles are better suited.