AN MD11F CAT III AUTOLAND COMPLETED ON A RWY COVERED WITH SNOW. UPON TURNING ONTO A TXWY THE #3 ENG FLAMED OUT.

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A CAT III AUTOLAND APCH WAS COMPLETED TO RWY 7R AT THE ZZZ ARPT. THE TIME WAS ROUGHLY XA00; WITH CEILING RPTED AS 500 FT WITH 1/2 MI VISIBILITY DUE TO SNOWFALL. THE TWR GAVE RVR THAT WAS LEGAL FOR THE APCH; AS WELL AS A PIREP FROM A KING AIR THAT THE BRAKING ACTION WAS POOR. RWY 7L WAS ALSO RPTED AS POOR BRAKING. DSCNT AND APCH WERE UNEVENTFUL; THE TOUCHDOWN WAS SMOOTH. THE ACFT WAS CONFIGURED FOR FLAPS 50 DEG LNDG. MAX AUTOBRAKES HAD BEEN SELECTED; DUE TO THE BRAKING ACTION LESS THAN GOOD. AT TOUCHDOWN THE BRAKES ACTIVATED AND THRUST REVERSE WAS INITIATED. THE NOSE OF THE ACFT WENT SLIGHTLY R OF CTRLINE AND WAS CORRECTED BY THE AUTOPLT; AND THEN WENT SLIGHTLY L OF CTRLINE AND WAS CORRECTED. THE RWY WAS COVERED BY SNOW; AND I FOUND THE BRAKING TO BE POOR. THE TXWY MARKINGS WERE PARTIALLY OBSCURED BY SNOW; AND THE RWY MARKINGS WERE COMPLETELY COVERED BY SNOW. RWY EDGE LIGHTS WERE VISIBLE AS WERE THE CTRLINE LIGHTS; WHILE THE CTRLINE LIGHTING DETERIORATED CONSIDERABLY THE FURTHER YOU WENT DOWN THE RWY. I COULD TELL THE BRAKING WAS POOR AND AFTER A CONSIDERABLE AMOUNT OF ROLLOUT; I DISCONNECTED THE AUTOBRAKES AND USED MANUAL BRAKING. REVERSE THRUST WAS USED FROM THE BEGINNING OF TOUCHDOWN TO JUST UNDER 80 KTS TO ENSURE THE ACFT WOULD STOP. THE ACFT WAS NOT SLOWED ENOUGH TO SAFELY LEAVE THE RWY UNTIL TXWY D. THE FO RPTED TO THE TWR THE BRAKING ACTION WAS POOR. AS THE ACFT LEFT THE RWY FOR TXWY D; THE FO NOTICED A LEVEL 2 ENG 3 RPM LOW LIGHT ILLUMINATED. HE AND THE RELIEF OFFICER RAN THE CHKLIST WHILE I TAXIED THE ACFT OFF THE RWY. THE CHKLIST WAS COMPLETED AND THE ENG WAS SECURED. FLAPS WERE LEFT EXTENDED FOR A CONTAMINATION CHK. ZZZ OPS WAS CALLED BY RADIO AND INFORMED OF THE ENG FLAMEOUT AND THE FLAP POS; AND ASKED TO HAVE MAINT MEET THE ACFT. THE CONTAMINATION CHK WAS COMPLETED; AND THE FLAPS WERE RAISED. I WROTE UP THE ENG FLAMEOUT ALONG WITH THE HIGHEST EGT OBSERVED OF 623 DEGS. WE THEN COMPLETED THE SHUT AND SECURE CHKLIST. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED MAINT FOUND THE ENG HAD INGESTED A LARGE AMOUNT OF SNOW. THE MAINT RPT DID NOT SPECIFY WHAT PART OF THE ENG THE INGESTION OF THE SNOW AFFECTED; ONLY SNOW CLEANED OUT. THE ENG DID GET A PERFORMANCE RUN AND WAS RETURNED TO SVC.