What was found
DESCENDING OUT OF FL450 THE RT ENGINE FLAMED OUT. THE EMERGENCY CHECKLIST WAS FOLLOWED AND AN EMERGENCY WAS DECLARED WITH ATC. AT FL200 AN ENGINE AIR START GENERATOR ASSIST WAS PERFORMED IAW THE CHECKLIST AND THE ENGINE STARTED AT APPROX 16,000 FT. ENGINE PARAMETERS WERE ALL NORMAL ACFT CONTINUED. THE LANDING WAS UNEVENTFUL. MX TROUBLESHOT THE DISCREPANCY WITH SUPPORT AND DETERMINED THAT THE FUEL CONTROL UNIT NEEDED TO BE REPLACED. THE FUEL CONTROL UNIT WAS REPLACED. ENGINE RUN, LEAK AND OPS CHECKS WERE GOOD. ACFT WAS RETURNED TO SERVICE AND A SUCCESSFUL OCF WAS PERFORMED.