The Raytheon Beechjet 400A was descending through flight level 390 when both of the engines flamed out and lost all power while operating in instrument meteorological conditions with convective storms in the area. The pilots, after several attempts, were able to get one engine restarted as the airplane was descending through 10,000 feet and diverted to a nearby airport. Testing of the engines immediately after the incident revealed that they were operating correctly. Testing of the fuel revealed that it conformed to the specifications for Jet A, but the fuel system icing inhibitor (FSII) was significantly below the required concentration. The investigation of two subsequent dual-engine flame out incidents revealed the FSII was not a factor. Convective weather can lift significant amounts of water into the upper atmosphere that then form ice crystals. Research indicates that the ice crystals can partially melt passing through the JT15D-5 engine fan that can then accrete to an internal compressor stator. When any accreted ice was shed from the stator vanes, it would pass through the high pressure compressor and could be picked up by the pressure sense line to the fuel control. Flight tests confirmed that sense line could go below freezing at low power settings at high altitude. Other tests showed that if the sense line was blocked and the power levers were retarded, the electronic engine control would reduce the fuel flow to reduce the power, but the sense pressure within the fuel control would be maintained. But when the blockage was cleared, the sudden reduction in the sense pressure in the fuel control would result in a reduction of the fuel flow at a rate that was much faster than a normal rapid power reduction and could result in the engine flaming out. Probable Cause: High-altitude ice crystals that had accreted on the compressor vanes and were ingested into the high pressure compressor when the pilots retarded the power levers causing compressor surges and flameouts of both engines. Contributing factors were 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.