The pilot reported he was unable to extend the flaps during his prelanding checks, despite several attempts. Turning onto base, the pilot noticed a commuter aircraft about to taxi to the active runway and decided to carry out a flapless landing. As power was reduced, during the turn onto final approach, an aural warning sounded. Thinking it was the stall warning, he increased power and the warning ceased. The approach was continued until power reduction at the flare when the warning again sounded as the aircraft settled onto the runway with the landing gear still retracted. The pilot stated that he failed to complete his prelanding checks and extend the landing gear after the flap failure. He also incorrectly identified the landing gear warning as the stall warning.