The pilot of the tailwheel equipped airplane reported that during the landing roll out with the tailwheel down, the tail of the airplane lifted back into the air, at that time he attempted to abort the landing. The pilot further reported that when the airplane became airborne the left wing dropped, then the right, both of which he countered. Subsequently, the left wing dropped again and struck the ground. The airplane exited the runway to the left and came to rest on its nose. The airplane sustained substantial damage to the left wing and aileron. After the accident, witnesses reported to the pilot that a dust devil had touched down in front of the airplane during the landing. The pilot reported that there were no pre impact mechanical failures or malfunctions with the airframe or engine that would have precluded normal operation.