The CFI was demonstrating a soft field takeoff. After lift-off the airplane settled back to the runway, then became airborne again. Control was lost, and the airplane settled into terrain adjacent to the runway. No discrepancies were found during the wreckage examination. The left flap was found deployed to about 10 deg due to impact damage, and the follow-up cable was slack. The remainder of the flap system was intact. This is consistent with flaps being in the up position at impact. Flaps are electrically driven through a jack screw to the right flap. The left flap is driven by a follow-up cable through the right flap jack screw; therefore the left flap cannot be driven to a position to which the right flap is not driven. The right flap was found in the up position. The recommended flap setting for a short field takeoff is 10 deg. According to the FAA Flight Training Handbook, during soft field takeoff the airplane can become airborne at an airspeed below safe climb speed due to the action of ground effect.