AFTER TKOF A B727 CREW TURNED IN ERROR TO A HDG CORRESPONDING TO THE WIND DIRECTION GIVEN AS PART OF TKOF CLRNC. THE TRACK CONFLICTED WITH TFC OFF OF A PARALLEL RWY. RADAR VECTORS FOLLOWED.

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THE FLT FROM ATL TO MIA WAS CLRED INTO POS AND HOLD AND THEN CLRED FOR TKOF ON RWY 9R IN ATL BEFORE THE ACFT STOPPED IN TKOF POS. THE FO READ THE CLRNC BACK AS RWY HDG; CLRED FOR TKOF. ATL TWR RPTED THE WINDS IN AN EXPEDITIOUS MANNER AS 060 DEGS AT APPROX 14 KTS. THE CAPT SAID; '060; CLRED FOR TKOF;' SET HIS HDG BUG TO 060 DEGS AND CALLED FOR THE BEFORE TKOF CHKLIST BELOW THE LINE. THE CAPT HAD MISTAKEN THE WIND DIRECTION FOR THE INITIAL HDG IN THE PROCESS OF ALIGNING THE ACFT AND RESPONDING TO THE CHKLIST. WHEN CLING THROUGH APPROX 2900 FT MSL; THE CAPT NOTICED THAT THE FO HAD NOT BEGUN THE TURN TO 060 DEGS AND STATED 'ZERO SIX ZERO' IN A NORMAL TONE OF VOICE. THE TWR INSTRUCTED THE FLT TO CONTACT DEP AS THE FO BEGAN APPROX A 15 DEG BANK L TURN TOWARD 060 DEGS; WHILE QUESTIONING THE CALL FOR THE TURN. THE CAPT CONTACTED ATL DEP; GAVE THE PASSING AND ASSIGNED ALTS AND STATED 'HDG 060 DEGS ASSIGNED' FOR THE PURPOSE OF CONFIRMATION. ATL DEP THEN ISSUED A R TURN TO 150 DEG THEN A L BACK TO 090 DEGS AS THE ACFT WAS NEARING A HDG OF 070 DEGS. HIS MISUNDERSTANDING PLACED THIS FLT IN CONFLICT WITH A B737 DEPARTING THE NORTH COMPLEX. SUPPLEMENTAL INFO FROM ACN 633163: THE CREW DISCUSSED THE TURN INSTRUCTIONS GIVEN UPON REACHING CRUISE ALT. AFTER LNDG AT MIA GND CTL RELAYED NAME; PHONE NUMBER AND REQUEST TO CALL ATL TWR. PROB CAUSED BY A MISPERCEPTION THAT WAS NOT VERBALIZED (AND SO NOT ADDRESSED BY CRM). MY QUERY REGARDING PROPER HDG DID NOT PRODUCE ANY UNCERTAINTY ON THE CAPT'S PART. DURING THIS BUSY PHASE OF FLT I CHOSE TO FOLLOW HIS INSTRUCTION TO TURN TO 060 DEGS. I WAS AWARE OF PARALLEL DEPS N OF US. A L TURN WAS AN UNLIKELY CLRNC. I SHOULD HAVE DEMANDED CLARIFICATION. IN THIS CASE A LATE TURN (IF PROVED WRONG) WOULD'VE BEEN PREFERABLE TO THE ACTION I TOOK.