There is no cheat code that specifically grants an "Army Uniform" in GTA Vice City. However, the cheat PROFESSIONALSKIT (entered during gameplay) spawns a suit, tie, and briefcase—a "professional" look that is the closest vanilla alternative to a uniform.
For the original PS2 and Xbox releases, the suit via PROFESSIONALSKIT remains your only in-game "uniform" cheat. No army fatigues, no camouflage—just Tommy Vercetti looking sharp in a business suit.