As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
DURING CLIMBOUT FROM RJTY AT FL390 NUMBER THREE ENGINE FLAMED OUT. THE CREW DESCENDED TO FL320 WITH IGNITERS IN BOTH AND OVERRIDE IN ALL ENGINES. APPROXIMATELY AT FL340 THE ENGINE RESTARTED, ALL INDICATIONS RETURNED TO NORMAL AND THE CREW CONTINUED THE FLIGHT TO WSAP, LANDING WITHOUT INCIDENT. MAINTENANCE INSPECTED THE ENGINE IAW CFM56 MM 71-00-00 FAULT TREE 51. ALL STATIC CHECKS WERE GOOD. THE FUEL FILTER WAS INSPECTED AND NO CONTAMINATION WAS FOUND. THE OPERATIONAL CHECK WAS GOOD AND THE AIRCRAFT WAS RETURNED TO SERVICE.