AFTER TROUBLESHOOTING A B767-300'S FAILED FLAP INDICATOR; THE ACFT LANDED WITH 5;300# OF FUEL. A MORE DIRECT RWY APCH WAS DENIED EVEN IN AN EMER STATE.

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WE WERE BEING SEQUENCED FOR ARR AND WERE TOLD TO SLOW TO 210 KTS. WHEN SELECTED FLAPS 1 DEG; GOT NO INDICATION OF FLAP MOVEMENT ON INDICATOR. DECLARED AN EMER WITH ATC AND ASKED FOR RADAR VECTORS TO WORK OUT PROB. THERE WERE NO EICAS/STATUS MESSAGES OR ASYMMETRY IN AIRPLANE MOVEMENT NOTED. WE WERE WITHIN FLAPS 5 DEGS SPD LIMIT SO SELECTED FLAPS 5 DEGS TO SEE IF WE WOULD GET AIRPLANE ATTITUDE CHANGE WITH FLAPS. AIRPLANE ACTED NORMAL FOR FLAP TRANSITION. CALLED CABIN TO HAVE FLT ATTENDANT CHK TRAILING EDGE FLAPS. A PLT TRAVELING IN THE CABIN DID THE CHK. FROM THE FEEL OF THE ACFT AND THE VISUAL RPT; WE BELIEVE WE HAD AN INOP FLAP INDICATOR. COM TO REACH DISPATCH WAS DIFFICULT; HAD TO EMER SATCOM CALL. HAD A PHONE PATCH WITH MAINT CTL; RESET INDICATOR CIRCUIT BREAKERS; FLAP INDICATOR REMAINED INOP. BRIEFED CHIEF PURSER OF PROB AND ISSUED A CABIN ADVISORY. THEY WERE TOLD THAT WE DECLARED AN EMER; NATURE OF THE PROB; AND WERE ISSUED A CABIN ADVISORY. THEY WERE ALSO TOLD TO EXPECT A NORMAL NG. SINCE FLAPS APPEARED TO FUNCTION PROPERLY; WE PLANNED FOR A NORMAL FLAP LNDG; WITH AWARENESS FOR ASYMMETRIES AND SPD MARGIN OF +10. WE POSITIONED THE PLT IN THE CABIN BEHIND THE WING; KEPT COM WITH FLT ATTENDANT AT MID CABIN; CONFIGURED EARLY; AND VERIFIED FLAP MOVEMENT VIA MID CABIN FLT ATTENDANT AND PLT OVER WING. HAD A NORMAL LNDG AND TAXI TO THE GATE. AS STATED BEFORE; IT WAS VERY DIFFICULT TO MAKE COM WITH COMPANY VIA NORMAL COMRDO DUE TO ALT. WE ALSO TRIED VIA ZZZ OPS UNSUCCESSFULLY. AFTER WE SENT EMER SATCOM CALL IT WAS FRUSTRATING TO BE PUT ON HOLD WHILE BEING CONNECTED TO OUR DISPATCHER. ATC MADE THIS TIME PERIOD COMPLICATED WITH MANY FREQ CHANGES; ALT CHANGES THAT WERE THEN CANCELED; THE VECTORING; AND FINALLY ISSUED A HOLD WITHIN 10 MI OF THE HOLD FIX. 1 CTLR ASKED IF WE WERE READY TO CONTINUE ON OUR FLT PLAN OR RETURN TO ZZZ. APPEARED TO BE A LACK OF COM BTWN THE CTLRS. AFTER WE WERE READY TO CONTINUE INBOUND TO LAND; WE WERE ASKED FOR A RWY PREFERENCE; WE TOLD THEM WE WERE SET UP FOR THE RWY XX; WE WERE THEN GIVEN VECTORS TO EXPECT RWY XX. A FEW MINS LATER; WE WERE TOLD THAT THEY WERE NO LONGER USING RWY XX FOR ARRS AND TO EXPECT RWY YY. WE TOLD THEM UNABLE AND HAD TO DECLARE MINIMUM FUEL STATE. THEY REPLIED THAT THOSE WERE THE RWYS IN USE AS IF THERE WAS NO OTHER CHOICE. WE TOLD THEM WE COULD ACCEPT Z; BUT WERE UNABLE LNDG N DUE TO FUEL STATE. WE HAD STARTED WITH 11.3 AT THE BEGINNING OF THIS PROB AND WERE NOW AT 6.5. WE DECIDED THAT DUE TO EARLY CONFIGN FOR LNDG AND THE DELAYS THAT WE HAD BEEN ENCOUNTERING DUE TO ATC THAT WE WOULD ONLY NOW ACCEPT AA'S FOR LNDG. WE WERE TOLD THAT THOSE WERE THE DEP RWYS. INSISTED THAT WAS ALL WE WOULD ACCEPT DUE TO FUEL LOAD. I FELT WE HAD NO PRIORITY HANDLING AS AN EMER ACFT. BLOCKED IN THE GATE WITH 5.3.