A Piaggio Avanti blew its two main gear tires during a runway incursion at Teterboro Airport on June 17. The Avanti, operated by Avantair, was cleared to depart Runway 24. Forty seconds later, Cirrus SR22 N6026K was cleared to depart Runway 19, which intersects Runway 24. The Avanti pilot saw the approaching aircraft, applied maximum braking and missed hitting the SR22 by 50 feet. The incident occurred during VMC conditions.