B-727 FREIGHTER EXPERIENCES FLAMEOUT OF #1 ENG AFTER LNDG. FUEL STARVATION.

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DISPATCHED WITH #1 FUEL TANK QUANTITY INDICATOR DEFERRED PER BOEING MEL. MAINT ADVISED THAT FUEL QUANTITY OF 9200 LBS WAS IN TANK #1. FUELING HAD BEEN ACCOMPLISHED USING TRANSFER OF KNOWN QUANTITY FROM TANK #2 AND VERIFIED BY DRIP STICK READINGS. FUEL ON BOARD WAS APPROX 28000 LBS. REQUIRED FUEL APPROX 19000 LBS AND FLT PLAN BURN ESTIMATED APPROX APPROX 10000 LBS TOTAL. DEPARTED CVG FOR BWI AND NOTED A LIGHT WING HVY TENDENCY WHICH GREW MORE PRONOUNCED DURING LNDG CONFIGN. THE PREVIOUS FLC HAD WRITTEN UP THE ACFT FOR OUT OF TRIM CONDITION. SO WE ASSUMED SAME. UPON LNDG THE #4 MAIN TIRE BLEW OUT. WE CLRED THE ACTIVE RWY AND PARKED THE ACFT ON A XING INACTIVE RWY; WHILE WE WAITED FOR ARPT OPS TO INSPECT OUR TIRES FOR DAMAGE. SHORTLY AFTER PARKING THE ACFT THE #1 ENG SPOOLED DOWN. SUDDENLY THE LATERAL IMBAL BECAME CLR. 5000 LBS HVY IN THE R SIDE CAUSED THE CTL WHEEL DEFLECTIONS AND THE HVY LOAD THAT BLEW THE TIRE. THERE WAS NO FUEL IN THE #1 TANK. NO MAINT WRITEUP WAS ENTERED INTO THE ACFT LOGBOOK REGARDING THE ENG BECAUSE THE FLT HAD BEEN TERMINATED (I.E.; MOVEMENT FOR THE PURPOSE OF FLT HAD CEASED) AND WE KNEW THAT THE CAUSE OF THE ENG FAILURE WAS A FUEL STARVATION SIT WHICH HAD BEEN PREVIOUSLY ADDRESSED IN THE DEFERRED FUEL GAUGE. SUPPLEMENTAL INFORMATION FROM ACN 265413: DSNDING INTO BWI AIRSPACE WE STARTED TO ENCOUNTER CLR STRUCTURAL ICING. ONCE CONFIGURED FOR LNDG AND ON FINAL APCH AT 140 KIAS; I NOTED AND RESPONDED TO THE CAPT THAT THE ACFT WAS FURTHER OUT OF LATERAL TRIM AND WAS REQUIRING MORE L RUDDER. I WAS CONCENTRATING ON THE APCH DUE TO THE WX CONDITIONS. WE HAD A L XWIND IN LIGHT FREEZING RAIN. WE MADE A FAIRLY LIGHT TOUCHDOWN ON CTRLINE. I LOWERED THE NOSE AND APPLIED BRAKES AND REVERSE THRUST. THE RWY APPEARED SLIPPERY. AFTER PASSING CTL TO THE CAPT. HE STARTED A SLOW TAXI AND NOTED THAT IT APPEARED WE HAD A R BLOWN MAIN TIRE AND CONFIRMED IT WITH TWR CTLR. WHILE PREPARING TO SHUT DOWN; THE #1 ENG SUDDENLY FLAMED OUT AND SHUT DOWN. WE CONTINUED SHUTTING DOWN ENGS #2 AND #3. THE SO HAD USED APPROVED FUEL FOR DISPATCH COMPUTATIONS PRIOR TO DEP AND HAD BURNED TANK TO ENG THE ENTIRE FLT TO KEEP FUEL BURN EVEN DUE TO THE DEFERRED FUEL GAUGE. THE ONLY CONCLUSION REMAINING IS THAT THE L FUEL TANK WAS IMBALANCED AND DID NOT HAVE THE FUEL REQUIRED; BASED ON THE TOTALS WE WERE GIVEN AND THAT CTL TRIM PROBS NEVER EXISTED.