AN ATX C550 FLC LANDED WITHOUT AUTH DURING A TRAINING FLT. THE RPTR ADMITS TO BEING TIRED.

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WE HAD ALREADY FLOWN A FLT IN THE LEAR 31 TO MOSES LAKE AND HAD RETURNED AT ABOUT XA30 LCL TIME. OUR CITATION II HAD RETURNED FROM HAVING SOME MAJOR MAINT (A LARGE DOOR INSTALLED) AND SINCE NONE OF US WERE CURRENT IN THE ACFT; THE COMPANY HAD DECIDED THAT WE SHOULD STAY AND GET 3 LNDGS AND APCHS EACH IN THE ACFT. ANOTHER PLT CAME IN TO WORK TO GET CHKED OUT WITH US. EACH ONE OF US WERE TYPED IN THE ACFT; QUALIFIED AS PIC AND HAD A HIGH LEVEL OF EXPERIENCE. WE TAXIED OUT ABOUT XD00; WITH THE 3 PLTS IN THE ACFT; 1 PLT IN THE BACK WAS CHK AIRMAN AND WAS ON THE INTERCOM. WE ARE BASED AT BFI AND WERE TO FLY OVER TO SEATAC AND DO OUR APCHS AND LNDGS. THE FIRST PLT DID 3 INST APCHS AND LNDGS (STOP AND GOES) FROM THE L SEAT WHILE I SERVED AS SIC FOR HIM. THEN WE SWITCHED HATS AND I DID MY 3 APCHS AND LNDGS (STOP AND GOES) FROM THE R SEAT AS PIC. IT WAS NOW ABOUT XD30; THERE WASN'T MUCH TFC AND WHILE I WAS TAXIING BACK FOR TKOF AT RWY 16L AT SEA THE CHK AIRMAN SWITCHED SEATS WITH THE OTHER PLT (IN THE L SEAT). HE DID THE TKOF AND WE CLBED OUT TO 5000 FT AND WERE VECTORED TO THE E FOR A DOWNWIND FOR AN ILS RWY 16R APCH; SIDESTEP TO THE L AND LAND ON RWY 16L (THEY HAD EARLIER SHUT DOWN RWY 16R). ON DOWNWIND; THERE WAS A LOT OF CHATTER IN THE COCKPIT AND I WAS BUSY DOING CHKLISTS AND I DID NOT HEAR THE PIC CALL APCH AND ASKED HIM TO COORDINATE WITH THE TWR TO DO A FULL STOP; A 180 DEG TURN AND TKOF TOWARD BFI FROM RWY 34R. WE WERE CLRED TO TURN BASE TO HDG 180 DEGS TO INTERCEPT THE LOC; CLRED FOR THE ILS RWY 16R APCH; SIDESTEP TO THE L; CONTACT TWR AT PARKS (LOM) AND EXPECT TO GET A 180 DEG ON THE RWY FROM TWR. I READ THE CLRNC BACK TO HIM AND WONDERED WHAT THIS STUFF WAS ABOUT A 180 DEG ON THE RWY. WE DIDN'T CONFIGURE FOR THE APCH LIKE USUAL; BECAUSE WE WERE DOWN TO ABOUT 1000 LBS OF FUEL AND WANTED TO CONSERVE AS MUCH FUEL AS WE COULD; SO HE WAITED TO MUCH LATER TO DROP APCH FLAPS AND GEAR. INSTEAD OF GETTING THE CHKLIST DONE PRIOR TO THE OM; WE WERE DOING THE CHKLIST AFTER THE OM INBOUND AND WOULD WAIT UNTIL SHORT FINAL TO DROP FULL FLAPS AND SIDESTEP TO THE L. SO INSTEAD OF FLAPS; TIME AND TALK AT THE OM INBOUND; I WAS BUSY DOING THE CHKLIST. THIS IS WHERE THE FATIGUE AND THE NON STANDARD INSTRUCTIONS FROM APCH CAME IN; 'EXPECT A 180 DEG ON THE RWY FROM TWR.' I THOUGHT I HAD TALKED TO TWR AND WE PROCEEDED IN AND LANDED ON RWY 16L; WITHOUT A CLRNC TO LAND. NOT ONLY HAD I MISSED IT; BUT BOTH OTHER PLTS MISSED IT AS WELL. WHEN I CALLED FOR A 180 DEG ON THE RWY; APCH CTL ANSWERED. I SWITCHED TO TWR; RECEIVED A CLRNC FOR THE 180 DEGS; WE TOOK OFF AND GOT VECTORS FOR AN INST APCH AND LNDG AT BFI.