The airline transport pilot was departing from a 960 foot-long, rough and uneven gravel airstrip, with three passengers and baggage during a Title 14, CFR Part 135 on-demand charter flight. The pilot reported that prior to starting the takeoff, he selected 10 degrees of flaps. During the takeoff roll, he selected 20 degrees flaps as the airplane reached rotation speed. The pilot said that the airplane failed to become airborne as it neared the end of the airstrip, and he aborted the takeoff run. He applied heavy braking, but was unable to stop the airplane before it went off the airstrip. The airplane's main landing gear wheels collided with a gravel bar, and both main landing gear legs collapsed. The airplane sustained structural damage to the wings, fuselage, and empennage. The pilot noted that there were no preaccident mechanical anomalies with the airplane.