The dual-engine flameout due to high-altitude ice crystals that had accreted onto the JT15D-5 engines' compressor vanes and were ingested into the engine when the pilots retarded the power levers, resulting in compressor surges and rapid reduction in fuel flow due to temporary ice blockage of the combustion pressure return line, and additionally preventing an in-flight restart. Contributing to the cause of the dual-engine flameout was the lack of training on the hazards of high-altitude ice crystals to gas turbine engines and guidance to the pilots to activate the engine anti-ice system in conditions where high-altitude ice crystals may exist.