ACR WDB ACKNOWLEDGED AN AMENDED CLRNC NEW SID BUT FAILED TO COMPLY.

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WE HAD BEEN CLRED BY KINGSTON FOR THE KINGSTON 2 DEP OFF RWY 12 ENRTE TO JFK. APCHING THE END OF THE TAXIWAY WE WERE CLRED FOR TKOF. WX WAS CLR AND VISIBILITY UNLIMITED. AS WE WERE STARTING THE TKOF ROLL THE TWR ASKED IF WE COULD CROSS THE KINGSTON VOR AT 9000 FT; AT LEAST THAT IS WHAT I UNDERSTOOD HIM TO SAY. WELL INTO THE TKOF ROLL HE CAME BACK WITH ANOTHER CLRNC. AT THIS POINT I WAS NOT PAYING MUCH ATTN TO HIM AND FIGURED HE WAS JUST REAFFIRMING THE 9000 FT AT KINGSTON VOR. I BELIEVE MY REPLY TO HIM WAS 'ROGER.' ONCE AIRBORNE WE STARTED THE KINGSTON 2 DEP AND ABOUT THE TIME WE GOT AROUND TO HDG 270 DEGS HE SAID THAT WE WERE SUPPOSED TO BE ON A 'SEKEL 2 DEP.' AT THAT TIME I REALIZED THAT HE HAD CLRED US FOR A DIFFERENT DEP DURING THE TKOF ROLL. WE MAINTAINED THE 270 DEG HDG AND FOLLOWED HIS INSTRUCTIONS. LOOKING BACK; I SHOULD NOT HAVE ACKNOWLEDGED HIS COMMENTS DURING THE TKOF ROLL; AS I'M SURE THIS LED HIM TO BELIEVE THAT WE UNDERSTOOD HIM. I WOULD; HOWEVER; SUGGEST THAT CHANGING A DEP DURING THE TKOF ROLL IS MUCH TOO LATE. IF IT IS NECESSARY AT THAT POINT TO CHANGE SOMETHING; THEN I BELIEVE THAT SPECIFIC INSTRUCTIONS SHOULD BE GIVEN; SUCH AS 'MAINTAIN RWY HDG TO 14 DME.' ALSO; THEY WATCHED US TURN THROUGH 150 DEGS BEFORE SAYING WE WERE ON THE WRONG DEP.