ATC GAVE THE WRONG DEP HEADING FOR A PLT OF AN SMA SEL DEPARTING AN ARPT NEAR A MIL BASE CAUSING 2 AIRBORNE CONFLICTS WITH 2 MIL KC135 TANKERS ON APCH.

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I WAS GOING TO DEPART BEC ON IFR FLT IN VFR CONDITIONS TO DEN. THE WINDS WERE SUCH THAT RWY 18 WAS IN USE AT BEC. BEC IS JUST NE OF AN AIR FORCE BASE THAT WAS ALSO USING RWY 18 WITH MULTIPLE KC135 ACFT IN THE TFC PATTERN. THE AFB TFC PATTERN OVERLIES THE TFC PATTERN AT BEC. BEC HAS A CTL TWR BUT IT WAS INOP AT THE TIME. I PICKED UP MY IFR CLRNC VIA AN RCO ON THE GND PRIOR TO TKOF. MY CLRNC INCLUDED ENTERING CTLED AIRSPACE HDG 220 DEGS AND I READ THAT BACK AND SET MY HEADING BUG TO 220 DEGS DURING READBACK. ON TKOF I INITIATED A CLBOUT AND NOTICED 1 KC135 OFF MY R AND KIND OF CLOSE SO I TURNED L A BIT TO GIVE HIM SOME ROOM TO DSND BEFORE ME AS HE WAS ON FINAL APCH TO ONE OF THE RWY 25'S AT THE AIR FORCE BASE. I FIGURED I COULD LET HIM GET BELOW ME AND THEN I COULD STILL TURN TO 220 DEGS BEFORE ENTERING CTLED AIRSPACE. AFTER THE TANKER MENTIONED ABOVE GOT BELOW MY FLT PATH A BIT I THEN TURNED BACK R TOWARDS HDG 220 DEGS. AS I WAS TURNING I SEE ANOTHER KC135 OFF TO MY R AT ABOUT MY ALT AND HE WAS MUCH CLOSER TO ME THAN THE FIRST. LIKE THE FIRST TANKER; HE WAS ALSO ON FINAL APCH TO THE AIR FORCE BASE. DEEMING THIS AN UNSAFE SIT I TURNED BACK TO THE L TO GIVE THE TANKER SOME MORE ROOM AND CALLED ATC AND QUERIED THEM REGARDING THE WISDOM OF THE 220 DEG HDG (WHICH WAS OBVIOUSLY GOING TO SEND ME RIGHT ACROSS THE APCH PATH OF THE RWYS AT THE AIR FORCE BASE). THE CTLR SAID SOMETHING TO THE EFFECT OF HE FORGOT I WAS DEPARTING BEC AND HAD GIVEN ME AN INCORRECT HEADING IN MY CLRNC AND I WAS TO NOW TURN L TO HDG 090 DEGS AND AWAY FROM THE AFB AND FURTHER CONFLICT. IF I HADN'T BEEN RUNNING BEHIND SCHEDULE AND BEEN LATE TAKING OFF; I MIGHT HAVE BEEN IN LESS OF A HURRY AND THOUGHT ABOUT THE HEADING GIVEN IN THE ORIGINAL CLRNC AND KNOWN IT NOT TO BE A GOOD IDEA.