Citation 560XL pilot reported leaving the Parking Brake set while initiating the takeoff roll; resulting in a loss of directional control; and a rejected takeoff.

Narrative

We rejected a takeoff at ZZZ on Runway XX. We received an IFR clearance with a void time of 5 minutes. A private Citation Jet had just landed an was rolling to the end of Runway XX to turn around before back taxiing to the ramp. We debated the ramp and taxied the short distance to the approach end of Runway XX. We got into position and waited. The jet took a considerable amount of time to back taxi off of the Runway the ramp. I set the parking brake. Finally the jet exited the Runway. We finished our takeoff flow items and set static power. Brakes were released and the aircraft immediately veered to. the right with left rudder applied. Power was immediately reduced to idle. I noticed the parking brake handle was pulled out. I pushed it back in and commenced a taxi. We heard and felt a thumping noise and vibration while taxiing and we elected to return to the ramp; We completely shut down the aircraft and inspected the main gear tires. Both tires had flat spots on them and the left main tire was partially shredded. We took pictures; called maintenance; and submitted write-ups. I missed pushing in the parking brake handle prior to engine spool up for a static takeoff. I originally set it while waiting on traffic to exit the Runway. Partial contributions to forgetting to release the park brake is the void time; leaving the ramp before our 15 minutes of run time limitations from ZZZ was up; and the setting of full power for a static takeoff. There are no park brake annunciators in the XLS.