The pilot stated that he made a normal landing in the tailwheel-equipped vintage bi-plane and planned to make a left, mid-field turn onto the taxiway. The wind was calm. When he applied the brakes to slow down, the airplane began to pull to the right and veer off the runway. The pilot applied full left rudder to compensate, but the airplane continued to veer right. As the airplane was about to depart the runway surface into the grass, the pilot increased brake pressure. When the right wheel contacted the grass, the brakes locked up and the tailwheel came off the ground. The airplane rolled forward onto its nose and flipped inverted resulting in substantial damage to the vertical stabilizer/rudder, and the right wing “N” strut. The pilot stated that there were no preaccident mechanical malfunctions or failures of the airplane that would have precluded normal operation.