There is no "flying cars" cheat code for Grand Theft Auto: Vice City Stories on PSP. The game does not include that cheat in its official list.
Rockstar omitted several cheats from the PSP port that existed on PS2. The closest alternatives:
Using unofficial trainers or CWCheat plugins can enable moon gravity or vehicle flight, but they risk save corruption and are unsupported.
Best approach: master the stunt jumps and unique jumps — they're designed to give that airborne thrill legitimately.