CPR LTT HAD AN ENG FLAME-OUT AT VERY HIGH CRUISE ALT.

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I AM PIC ON FALCON 20'S. ON OCT/XX/94 I WAS PIC OF A FALCON 20; ENRTE TO SANTA ANA. AS THE FLT PROGRESSED OVER THE ROCKIES WE ENCOUNTERED INCREASING HEADWINDS WHILE AT FL350. WE CLBED TO FL390 AFTER VERIFYING THE WINDS WERE THE SAME AT 390. AS THOSE WINDS INCREASED AND IT BECAME APPARENT WE WOULD LAND AT SANTA ANA WITH ONLY 40 MIN OF FUEL RESERVE; WE DECIDED TO CLB TO 410. WE HAD VERIFIED WITH PERFORMANCE CHARTS THAT OUR WT AND OUTSIDE TEMP WOULD ALLOW US TO GO TO 410. WE ARRIVED AT 410 AT A SPD OF .67 OR 197 KTS. WE HAD BEEN AT THIS ALT FOR ABOUT 10 MIN WHEN THE L ENG FLAMED OUT. WE ADVISED ATC AND DSNDED TO FL250. AT FL270 WE INITIATED A SUCCESSFUL RELIGHT AND CONTINUED TO LAS VEGAS WITHOUT ANY INCIDENT. WE NOTIFIED THE NTSB THE NEXT DAY AND THEY ADVISED US WE WERE NOT OBLIGATED TO NOTIFY THE FAA OR NTSB. NO FAR'S WERE BROKEN DURING THIS FLT. THE ENG HAS BEEN DISASSEMBLED AND VISUALLY INSPECTED AT THIS POINT. THEY FEEL AT THIS POINT THAT DUE TO AT LEAST 2 FUEL NOZZLES HAVING A COKING AROUND THEM THE SPRAY PATTERN WAS ALTERED. THIS CAUSED HOT SPOTS ON THE FIRST TURBINE NOZZLE AND ULTIMATELY FATIGUE FAILURE.