As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
AIRCRAFT EN ROUTE FROM MMV TO DKB RT ENGINE FLAME-OUT CLIMBING THROUGH FL410 TO 430, DESCENT TO FL250 PERFORMED AIR START ALL INDICATIONS NORMAL CONTINUED FLT. AT DESTINATION CREW INSPECTED ENGINE, NO DAMAGE NOTED. WILL UPDATE WHEN AIRCRAFT AT MAINTENANCE BASE.