LOSS OF SEPARATION BTWN AN ACR MD88 ON MISSED APCH FOR RWY 4R AND AN ACR B767 ON DEP FROM RWY 4L. THE DEP AND MISSED APCH PROCS REQUIRED BOTH ACFT TO TURN TO THE SAME HEADING AND CLB.

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WE WERE ON APCH (ILS) RWY 4R WHEN ON SHORT FINAL WE ENCOUNTERED WAKE TURB FROM THE PRECEDING ACFT. I BEGAN THE PUBLISHED MISSED APCH CLB TO 500 FT THEN CLBING R TURN TO 4000 FT VIA 100 DEGS AND V-44 DPK VOR AND HOLD. AT APPROX 1000 FT AND AFTER FO TOLD TWR WE WERE MISSED APCH; TWR TOLD US TO STOP CLB. I LEVELED THE ACFT AT APPROX 1000-1300 FT AND THEN DSNDED BACK TO APPROX 1000 FT. I DO NOT RECALL A TCASII RA/TA ALERT. A FEW MOMENTS AFTER THIS WE WERE TOLD TO CLB AND GIVEN VECTORS. AFTER I RETURNED HOME THE NEXT DAY I GOT A CALL FROM MY UNION SAYING ACR Y CAPT WAS FILING A NEAR MISS AT JFK. THIS CAPT CALLED ME AND SAID HE WAS TAKING OFF JFK RWY 4L. HIS DEP WAS TO TURN TO 100 DEGS AND CLB TO 5000 FT. HE GOT A TCASII RA AND FOLLOWED THE CLB PROMPT. HE SAID HIS TCASII SHOWED MY ACFT WAS 100 FT DIRECTLY BELOW HIS AND STAYED THERE UNTIL HE WAS AT APPROX 2300 FT. AFTER ALL THIS HE CALLED AND TALKED TO A TWR SUPVR WHO THEN SAID TWR WAS AT FAULT AND THEY SHOULD HAVE DELAYED THE ACR Y TKOF TO AVOID THE OBVIOUS CONFLICT OF A POSSIBLE MISSED APCH FROM RWY 4R. TO AVOID A FUTURE CONFLICT; THE RWY 4L DEP SHOULD BE CHANGED SO AS NOT TO CONFLICT WITH THE RWY 4R MISSED APCH. OTHERWISE; YOU WILL HAVE 2 ACFT IN THE SAME PIECE OF SKY AGAIN. IF WE HAD NOT BEEN BACK IN THE CLOUDS AGAIN WE WOULD HAVE SEEN EACH OTHER AND AVOIDED THIS CONFLICT. AS I SAID EARLIER I DID NOT KNOW OF THIS CLOSE CONFLICT UNTIL LATER THE NEXT DAY. NO ONE SAID ANYTHING ABOUT IT AT THE TIME. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR INDICATED THEY WERE ABOUT 200 FT WHEN THEY EXECUTED THE MISSED APCH AFTER THEIR ACFT WAS ROLLED FROM WAKE TURB FROM THE PRECEDING ACFT WHICH RPTR THOUGHT WAS A B767. RPTR INDICATED THAT HE WAS SUBSEQUENTLY CONTACTED BY SOMEONE FROM THE FAA FOR INFO ON THE INCIDENT. SUPPLEMENTAL INFO FROM ACN 390495: TWR REQUESTED WE FLY 180 KTS TO THE MARKER; BEHIND A HVY IN IFR CONDITIONS (BAD IDEA ON THEIR PART). APPARENTLY TWR DID NOT ALLOW FOR THE POSSIBILITY THAT OUR MISSED APCH WOULD CONFLICT WITH THE TKOF SEQUENCES. SUPPLEMENTAL INFO FROM ACN 390811: TOOK OFF ON RWY 4L AND I WAS FLYING KENNEDY 7 DEP. ABOUT 1000 FT INTO THE CLB WE RECEIVED AN RA TO MONITOR VVI. AT THAT TIME THE VVI INDICATED RED DOTS TO 2000 FPM AND GREEN DOTS FROM 2000 FPM TO 2300 FPM. ACFT WAS MAINTAINED IN THE GREEN RANGE. AT SOME TIME DURING THE DEP CAPT TOLD TWR WE HAD A TCASII ALERT (ABOUT 1500 FT) AND TWR THEN SAID MAINTAIN RWY HEADING AND THEY WERE TAKING CARE OF IT. WE WERE WELL INTO THE DEPICTED DEP. TWR THEN TOLD US TO MAINTAIN 2000 FT. WE ACKNOWLEDGED THE TURN TO RWY HEADING BUT NOTICED OUR ALT WAS 2100 FT AND TCASII SHOWED A MERGED RED SQUARE 100 FT BELOW US. WE IGNORED THE ALT FROM TWR AND CONTINUED TO FOLLOW THE COMMANDED VVI GREEN RANGE. (TO LEVEL OFF WOULD HAVE CAUSED A PROBABLE MIDAIR.) WE WERE BARELY ABLE TO MAINTAIN THE 2300 FPM RATE OF CLB AND AIRSPD WAS APCHING V2 WITH NO STALL INDICATION; FLAPS 5 DEGS AND MAX PWR. THE MERGED TARGET REMAINED 100 FT BELOW US DURING THE ENTIRE RA; ABOUT 15-20 SECONDS; INDICATING THE TARGET WAS THE SAME CLB RATE AS US 100 FT BELOW. AFTER THE CONFLICT WAS CLR WE CONTINUED TURN TO RWY HEADING AND DSNDED TO 2000 FT. WENT TO DEP AND ASKED ABOUT THE RA. THEY GAVE US TWR PHONE AND CAPT CALLED ON AIR PHONE. AN MD80 WENT MISSED OFF RWY 4R AND THE MISSED PROCS ARE ALMOST IDENTICAL TO JFK 7 DEP. TWR CHIEF APOLOGIZED AND SAID TWR SHOULD HAVE DELAYED OUR TKOF. AS RWYS 4L AND 4R ARE ON DIFFERENT FREQ; CTLRS DID NOT COORDINATE IN TIME. ENTIRE INCIDENT FLOWN IMC. THANKS.