As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
ACFT ROUTE FROM FNT TO ADS CLIMBING THROUGH FL398 FOR FL430 RT ENGINE FLAME-OUT, REQUEST LOWER ALT FL260. ENGINE RESTARTED AND CLIMB BACK TO FL390 PROCEEDED TO ADS. MAINTENANCE AT ADS PERFORMED FLAME-OUT INSPECTION PER THE GE M/M AND PERFORMED ENGINES RUNS, NO DEFECTS NOTED AT THIS TIME.