A DA20 CAPT RPTED INCREASED HEADWINDS; AND ATC IMPOSED LOWER ALT FLYING; CAUSED HIM TO DECLARE MINIMUM FUEL AND DIVERT TO TZR FOR RE-FUELING. DURING THE COURSE OF THIS DIVERSION; THE R ENG FLAMED OUT; BUT WAS RESTARTED.

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DURING OUR FLT TO TZR; WE EXPERIENCED STRONGER THAN FORECAST HEADWINDS. FURTHER; ZID KEPT US AT A LOWER ALT THEN WE HAD FILED; WHICH ALSO CONTRIBUTED TO GREATER FUEL BURN THAN HAD BEEN PLANNED. I DECLARED A MINIMUM FUEL TO AVOID ANY FURTHER DELAYS; ONCE WE WERE SENT OVER TO CMH. ATC ASSIGNED US FL240. WE STARTED DSCNT FROM FL310 TO FL240. AT FL260; I EXPERIENCED THE R ENG FLAME OUT. I IMMEDIATELY TOLD MY FO TO PULL OUT THE EMER CHKLIST AND ALSO NOTIFY ATC OF OUR SIT AT HAND. WE WERE BOTH EXTREMELY BUSY DURING THE RESTART CHKLIST; AND ATC WAS ASKING US QUESTIONS; WHICH INTERRUPTED US IN DOING THE CHKLIST. FURTHERMORE; I TOLD HIM TO TURN ON THE IGNITOR ON THE L ENG; JUST AS A PRECAUTION. IF WE DO LOSE THE L ENG; DECLARE AN EMER. BUT; WE WERE ABLE TO RESTART OUR R ENG AND LANDED SAFELY WITH BOTH ENGS. DURING TAXIING; GND CTL; ON INSTRUCTIONS FROM ARPT FIRE DEPT; TOLD US TO STOP; BECAUSE THERE WERE FLAMES COMING OUT OF OUR R ENG. I IMMEDIATELY PULLED THE R FUEL T-HANDLE AND SHUT DOWN BOTH ENGS. THE TZR FIRE DEPT THOROUGHLY EXAMINED BOTH OUR ENGS; AND AFTER FINDING NOTHING WRONG; GAVE US THE OK TO PARK. UPON TALKING TO THE ARPT MGR; HE ASKED ME IF WE HAD DUAL ENG FLAMEOUT. I ADVISED HIM; NO; ONLY OUR R ENG FLAMED OUT AND THE DUAL ENG FAILURE WAS A MISCOM.