General aviation pilot reported they failed to extend the landing gear resulting in a gear up landing.

Narrative

Approaching ZZZ [airport] ZZZ Approach handed me over to ZZZ tower. Upon initial contact with ZZZ tower they requested that I enter a left downwind for runway XXL and report 3 miles southeast of the field. ATC issued several traffic advisories due to traffic in the immediate area. The weather was reporting winds out of the southeast with gusts up to 19 knots. Due to the gusty winds; I opted for a flaps 20 approach and landing. While configuring; I ran the checklists but became distracted with ATC communications and somehow missed landing gear extension. Approach was bumpy with fluctuating airspeeds requiring more power than normal. During the approach the gear up warning system did not activate. Everything seamed normal until flare and touchdown when I quickly became aware the gear was not extended. I secured the aircraft and waited for emergency services to arrive. As a result of this incident no injuries were sustained. In retrospect; I believe the contributing factors were the wind conditions requiring lower flap setting and higher power setting for the approach and landing; which may explain why the gear warning system did not activate. In addition with my distraction with ATC and traffic; I did not back up the landing checklist with a GUMPS check technic (GAS; UNDERCARRIAGE; MIXTURE; PROPELLER.) I allowed myself to deviate from the number one priority-FLY THE AIRPLANE. In other words aviate navigate communicate. Reflecting on the occurrence; I believe I selected the correct approach and landing configuration for the existing conditions; however; I allowed myself to become distracted with traffic and ATC communications causing me to deviate from the number one priority- FLY THE AIRPLANE. Besides going through all checklists in the future; I will also as a final safety check; conduct the GUMPS technic at a minimum of 1000 feet; 500 feet; and prior to touchdown. This is a humbling and painful experience; which I feel in the long run will make me a better pilot. A valuable lesson I will never forget. I will always apply the three basic rules of flying; Aviate Navigate; Communicate as well as the proven GUMPS technic.