A B737 FLT CREW ABORTS THEIR TKOF WHEN THE CREW HEARS THE ACFT CONFIGN WARNING HORN ALERTS THEM TO A PROB AT MDW; IL.

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DEPARTING RWY 31C MIDWAY; TKOF WARNING HORN SOUNDED DUE TO FLAPS NOT EXTENDED. BACKGROUND: MDW HAD SEVERAL GND STOPS DUE TO STRONG WINDS. WE ARRIVED LATE AFTER HOLDING AT THE GATE IN OUR PREVIOUS CITY. OUR PREFLT PLANNING FOR DEP FROM MDW WAS VERY DETAILED AND NOT RUSHED. WE BRIEFED WINDSHEAR; ADVERSE PROFILE LIMITS FOR TKOF AND CALCULATED FLAPS 15 DEGS SINGLE ENG RETURN DATA. WE TALKED ABOUT USING ORD FOR OUR SINGLE ENG DIVERT. WE PUSHED BACK NORMALLY; STARTED OUR ENGS AND CLRED THE GND CREW. WE ALSO HAD A JUMPSEATER (COMMUTER). THE TIME OF DAY WAS EARLY EVENING CENTRAL AND IT WAS DARK. NORMALLY I FLY AM'S; HOWEVER; THIS WAS A TRIP I TOOK; SO I COULD GO SEE A FRIEND. I HAD BEEN UP AT XA15. MY FO HAD BEEN RECENTLY DISPLACED TO THE R SEAT FROM CAPT AND WAS ON HIS FIRST TRIP BACK AS AN FO (THIS WAS HIS 7TH LEG). MY FATIGUE; HIS REQUALIFICATION AND NIGHTTIME. AFTER CLRING THE GND CREW; I THOUGHT FOR SURE I CALLED FOR FLAPS 5 DEGS. WE DID DO THE PREFLT CHKLIST BECAUSE I REMEMBER CHANGING STABILIZER TRIM AND CHKING THE JUMPSEATER'S SHOULDER HARNESS. WHAT I DID NOT DO WAS TOUCH THE FLAP HANDLE; WHICH IS MY NORMAL PATTERN. MY MAIN FOCUS FOR TKOF WAS THE WIND. THE POS INDICATOR DID NOT REGISTER EITHER. ONCE AGAIN; WE DID NOT HURRY. WHEN CLRED FOR TKOF; AFTER THE 'BELOW THE LINE CHK;' AS I STRAIGHTENED OUT ON CTRLINE; I PUSHED THE THROTTLES UP AND GOT THE WARNING HORN. WE TOLD TWR WE WERE ABORTING (15 KTS). FATIGUE; NIGHT OPS FOR ME; A RETURN TO R SEAT FOR THE FO; AND A FOCUS ON THE WINDSHEAR CAUGHT US. I HAD JUST COME OFF A 3-DAY AM PRIOR TO THIS PM TRIP.