B757-200 CREW HAD A FLAP OVERSPD.

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UPON DEP FROM MDW ENRTE TO LGA AT NIGHT IMC; WE FAILED TO RETRACT FLAPS FROM 1 DEG TO 0 DEGS. THIS PROB; I BELIEVE; CAME ABOUT DUE TO A NONSTANDARD DEP; SEVERAL TFC CALLS ON DEP; AND A BREAKDOWN OF COM BTWN THE CAPT AND FO. AFTER TKOF; WE WERE REQUIRED TO PERFORM A R 165 DEG TURN (CLBING; NIGHT IMC). I WAS HAND FLYING AND CALLED FOR FLAPS ON SCHEDULE. UPON CALLING 'FLAPS UP' CLB CHKLIST; I CONTINUED TO ACCELERATE. I NOTICED I COULD NOT ACCELERATE TO 250 KTS AND VNAV WINDOW WAS OPEN AT 240 KTS. I WAS PERPLEXED. MY FO STARTED SELECTING DIFFERENT MODES ON THE MCP. AGAIN; THINKING I HAD AN AIRSPD PROB; I CONTINUED TO TRY TO ACCELERATE. AS I LOWERED THE NOSE AND STILL WOULD NOT ACCELERATE; I NOTICED THE FLAPS WERE AT THE 1 DEG POS. IN MY ATTEMPT TO ACCELERATE; I OVERSPD THE FLAPS BTWN 10-15 KTS. FLAPS RETRACTED OK AND EXTENDED OK UPON ARR. (NO PROC FOR FLAP OVERSPD ON B757). I NOTED THE OVERSPD IN THE LOGBOOK; BRIEFED MAINT CTL. I BELIEVE THIS WAS CAUSED TO A BREAKDOWN IN COM BTWN MYSELF AND MY FO. THEN WAS FURTHER COMPOUNDED BY HIS DIAGNOSING THE PROB.