A CHALLENGER FLC LOST SEPARATION WHILE ON RADAR VECTORS NEAR JFK.

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WE RECEIVED 2 OR 3 RADAR VECTORS FROM THE CTR CTLR. WE WERE ADVISED THAT THE VECTORS WERE 'FOR TFC.' WE COMPLIED WITH EACH OF THE HDG CHANGES IMMEDIATELY. HOWEVER; AT ONE POINT THERE WAS A LOSS OF SEPARATION; DUE TO CTLR ERROR; WHEN ANOTHER ACFT ALSO OPERATING UNDER IFR CAME WITHIN 2 - 2 1/2 MI OF US AND 500 FT BELOW US. I WOULD SUGGEST THAT MORE TRAINING FOR THE CTLR IS IN ORDER. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR WAS ALERTED TO A POSSIBLE VIOLATION. IT WAS ALLEGED THAT THE FLC WAS SLOW TO RESPOND TO THE VECTOR HDGS. WHEN ASKED FOR THE TAPES; AND OTHER PERTINENT INFO; THE RPTR WAS TOLD IT WOULD BE COMING TO HIM. AFTER SEVERAL WKS THE RPTR WAS TOLD THAT AFTER FURTHER REVIEW THIS WAS VIEWED AS A NON EVENT. WISHING TO BE SURE THAT NOTHING WAS LEFT ON THE FLC'S RECORD; THE RPTR MADE ANOTHER TELEPHONE CALL TO THE FAA. DURING THIS CALL THE RPTR WAS TOLD THAT NO ACTION WOULD BE TAKEN AGAINST THE FLC AND THAT THE CTLR HAD BEEN GIVEN ADDITIONAL TRAINING. A THIRD PARTY CONTACTED THE RPTR AND SUGGESTED THEY HAD KNOWLEDGE THE THREAT OF A VIOLATION WAS BASED ON THE CTLR'S RPT KNOWN TO BE FALSE BY THE THIRD PARTY. THE RPTR ASSUMED THAT FURTHER INVESTIGATION OF THAT RPT DISCOVERED THE ACTUAL FACTS WHICH CLRED THE FLC.