LTT CARGO JET ENG FLAMEOUT DURING HIGH ALT CLB. RESTARTED AT A LOWER ALT.

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ATC REQUESTED A CLB FROM FL370 TO FL390 DUE TO CONVERGING TFC AT FL370. I CHKED THE PERFORMANCE CHARTS; AND WE WERE RIGHT AT THE MAX WT AT THE CONDITIONS TO MAINTAIN FL390; SO I ACCEPTED THE CLB. UPON CLBING THROUGH FL380; ATC ISSUED A TIME RESTR TO BE LEVEL AT FL390. I WAS JUST STARTING TO LEVEL AT FL390 WITH ABOUT 10 SECONDS LEFT ON THE TIME RESTR WHEN THE R ENG FLAMED OUT. I ADVISED ATC OF THE SIT; AND THAT WE WERE UNABLE TO MAINTAIN FL390. ATC REQUESTED A 30 DEG L TURN IF ABLE; AND I COMPLIED. I AM UNCERTAIN IF ATC REQUESTED A TURN FROM THE CONVERGING TFC. WE NEVER ESTABLISHED VISUAL CONTACT WITH THE TFC; BUT THEY RPTED CONTACT WITH US VIA TCASII AND INFORMED ATC THAT WE PASSED BEHIND THEM. I DO NOT BELIEVE THAT TFC SEPARATION WAS EVER COMPROMISED; BUT I AM NOT CERTAIN. I BELIEVE THAT GIVEN THE CONDITIONS; IF ATC HAD INFORMED ME OF THE TIME RESTR WHEN THEY ISSUED THE CLB INSTRUCTIONS; I WOULD HAVE TOLD THEM I WAS UNABLE. IN THE FUTURE; I WILL NOT HESITATE TO ASK ABOUT ANY POSSIBLE TIME RESTRS FOR A CLB. WE HAD TO DSND TO FL270 TO ENTER THE RELIGHT ENVELOPE. THE ENG WAS STARTED; AND THE FLT CONTINUED NORMALLY. I BELIEVE THE FLAMEOUT WAS CAUSED BY TURB COMBINED WITH A HIGH ANGLE OF ATTACK.