WHILE WORKING A TE FLAP ASYMMETRY CHECKLIST A B767 CREW FAILED TO CONTACT THE TOWER FOR A LANDING CLRNC.

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B767 WAS LANDED WITHOUT CONFIRMING LNDG CLRNC WITH TWR. APCH HANDED ACFT OVER TO TWR FREQ. ALL 3 PLTS WERE OCCUPIED WITH A TRAILING EDGE DISAGREEMENT STATUS MESSAGE THAT HAD JUST OCCURRED AT THE FAF. PF WAS IN THE L SEAT RECEIVING A CHK FLT. INSTRUCTOR PLT (LINE CHK AIRMAN) WAS IN THE R SEAT (PM) AND I WAS RELIEF PLT IN THE JUMPSEAT. THE CAPT SHOULD HAVE CALLED FOR A MISSED APCH AS SOON AS THE FLAP PROB OCCURRED. INSTEAD ALL 3 PLTS TRIED TO HANDLE THE SITUATION WHILE CONTINUING THE APCH FROM THE FAF INBOUND. CONFUSION WITH THE VERBIAGE CONTAINED IN THE QUICK REF MANUAL REQUIRED THE PM TO BE DRAWN FROM HIS DUTIES AS PM AND TALKING WITH ATC; TO A DISCUSSION AS TO THE PROPER FLAP SETTING; WITH THE RELIEF PLT READING FROM THE QRM. THIS DISTR RESULTED IN ALL 3 PLTS MISSING THE FACT THAT THE LNDG CLRNC HAD NOT BEEN RECEIVED. IN ADDITION WE ALL MISSED OUR '1000 FT CLRED TO LAND' CALL AS WELL AS THE LNDG CHKLIST. THE SOLUTION TO THIS OCCURRENCE SEEMS SIMPLE. 1) CREATE TIME TO PROPERLY HANDLE THE PROB. 2) CONFIRM WITH EACH OTHER THE MEANING OF THE QRM (QUICK REF MANUAL). 3) USE CHKLISTS. 4) MAINTAIN CONSISTENT HABIT PATTERNS; IE; TAXI LIGHT ON WHEN LNDG CLRNC IS ISSUED. 5) ASSIGN TASKS TO EACH PLT; IE; WHO'S FLYING THE JET. WE HAD ALL THE TOOLS WE JUST DIDN'T USE THEM. SUPPLEMENTAL INFO FROM ACN 755586: AFTER LNDG AT ZZZ I REALIZED WE DID NOT CHANGE TO TWR FREQ; SO WE DID NOT OBTAIN A LNDG CLRNC. AFTER CLR OF RWY TWR ASK TO CALL HIM. I CALLED AND TOLD HIM I REALIZED WHAT WE HAD DONE. I EXPLAINED TO HIM WE HAD A FLAP MALFUNCTION (TRAILING EDGE FLAP) MESSAGE AND WERE WORKING THE ABNORMAL CHKLIST AND OVERLOOKED CONTACTING THE TWR. THE TWR CTLR SAID HE JUST WANTED ME TO KNOW WHAT WE HAD DONE AND IT WOULD NOT BE A PROB. NO RPT WAS TO BE SUBMITTED.