B737-800 FLC AT FL390 ALMOST FOILS CTLR'S PLANS AT ZKC FOR OPPOSITE DIRECTION; SAME ALT TFC SEPARATION WHEN THEY TURN TO 260 DEGS VERSUS THE CLRNC FOR 220 DEGS; 20 NM E OF SGF VOR; MO.

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IN CRUISE FLT AT FL390 ATC (ZKC) SAID 'FLY HDG 220 DEGS FOR TFC.' I READ BACK THE INSTRUCTIONS AND THE FO (PF) CHANGED THE ACFT HDG WITH THE HDG SELECTOR. WHILE TURNING; I LOOKED OUTSIDE AND SAW A DISTANT ACFT AT MY 11 O'CLOCK POS AND ASSUMED THAT THIS WAS THE TFC WE WERE TURNING FOR. I THEN WENT BACK TO FILLING OUT THE FLC LOGBOOK. APPROX 20-25 SECONDS LATER ATC ASKED TO VERIFY OUR HDG. I THEN REPLIED; 'HDG 260 DEGS; NOT REALIZING THAT THE FO HAD TURNED TO THE WRONG HDG. ATC THEN SAID 'THAT'S NOT THE HDG I TOLD YOU; BUT MAINTAIN 260 DEGS.' THEN ATC TOLD ANOTHER ACFT TO CHANGE ITS HDG. WE HAD NO TCASII ALERTS. APPROX 25-30 SECONDS AFTER THE INCIDENT; ATC CLRED US DIRECT TO A WAYPOINT ON OUR FLT PLAN. 1) FATIGUE WAS A CONTRIBUTING FACTOR; BECAUSE BOTH CREW MEMBERS WERE ON DAY 4 OF A 4 DAY TRIP AND HAD EARLY SHOW TIMES THE PREVIOUS DAYS. ON THIS DAY; BOTH CREW MEMBERS WOKE UP AT XA00 FOR A XB00 SHOW TIME. 2) ALSO CONTRIBUTING WAS ME FILLING OUT PAPERWORK IN CRUISE FLT. 3) I HAD BEEN FLYING WITH THIS FO ALL MONTH AND HE HAD NEVER HAD ANY PROBS FOLLOWING ATC INSTRUCTIONS. I HAD THE PRECONCEPTION THAT HE WOULD FOLLOW AN ATC CLRNC.