There are no cheat codes for flying cars in GTA: Liberty City Stories on PS2. The game simply does not feature flying cars or aircraft as part of its mechanics, so no such cheats exist.
Other cheats exist (infinite health, armor, weapons, spawn vehicles), but flying vehicles were not introduced until GTA: San Andreas (hydra, etc.) and later titles. Liberty City Stories stays grounded.
For a full list of actual cheats, consult a reputable cheat database like GameFAQs or CheatCC.