The 1,730-hour flight instructor and a student pilot performed a normal engine run-up in a twin-engine airplane prior to a local training flight. The run-up did not reveal any anomalies and the airplane was clear to taxi to runway 35L. The right engine lost power while the airplane was holding short to take the active runway. The student pilot attempted to restart the right engine when he noticed "flames coming from the bottom of the engine cowling." The flight instructor and the student pilot exited the airplane through the cabin door without injuries. Airport rescue and fire fighting (ARFF) personnel responded to the aircraft fire and extinguished the fire. A Federal Aviation Administration (FAA) inspector, who responded to the scene, reported that the right engine nacelle sustained structural damage as result of the engine fire. Additionally, the inspector found the exhaust stack for the number one cylinder had separated. The inspector also reported that the braided fuel line leaked when the line was pressure tested.