A B757 DEPARTING FROM BFI REJECTED TKOF OBSERVING DC8 CROSSING RWY DOWN FIELD.

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CLRED ON TO HOLD ON RWY 13R. FO WAS MAKING TKOF. WE WERE CLRED FOR TKOF AND BEGAN ROLLING. AFTER THE 80 KT CALL; I NOTICED AN ACFT THAT APPEARED TO BE HOLDING SHORT OF RWY 13R AT TXWY A7. I CHKED INSIDE ONCE MORE AND WHEN I LOOKED UP THE DC8 WAS MOVING FROM LEFT TO RIGHT ACROSS THE RWY IN OUR PATH. WE PERFORMED A REJECTED TKOF AND STOPPED APPROX 200 FT SHORT OF THE ACFT WHICH STILL HAD HALF THE FUSELAGE IN FRONT OF US. THE TWR MADE NO CALL TO US. THE DC8 APPARENTLY NEVER SAW US BECAUSE IT MAINTAINED THE SAME TAXI SPEED WHILE CROSSING THE RWY. REJECT SPEED WAS 110 KTS; BFI TWR INFORMED US THE DC8 WAS ONLY CLRED TO HOLD SHORT AT TXWY A7. SUPPLEMENTAL INFO FROM ACN 635844: FO CALLED FOR TAXI AND WAS CLRED TO RWY 13R VIA TXWYS A7 AND BRAVO. HE READ BACK CLRNC. THAT CLRNC CROSSES BOTH 13L AND 13R. WE BEGAN TAXI; VERY SHORTLY WE ARRIVED AT RWY 13R AND NOTICED AN ACFT HOLDING IN POSITION ON RWY 13R. I INSTRUCTED MY FO TO KEEP AN EYE ON THAT ACFT AS WE STARTED TO CROSS. ABOUT HALFWAY ACROSS WE BOTH DETERMINED THAT THE ACFT WAS MOVING; SO I ADDED MORE THRUST TO CLR THE RWY AS SOON AS POSSIBLE. AFTER CLRING; OBSERVED ACFT DISAPPEARING BEHIND US. AT THAT TIME; GND CTL ASKED IF WE KNEW WE WERE SUPPOSED TO HOLD SHORT OF RWY 13R. WE ANSWERED THAT WE HAD NOT BEEN GIVEN THAT INSTRUCTION. WE WERE THEN CLRED TO CONTINUE TAXI TO RWY 13R. I BELIEVE THAT WE WERE GIVEN OUR TAXI INSTRUCTION BY MISTAKE OR THE GND CTLR HAD NOT COORDINATED WITH THE TWR CTLR WHO WAS HANDLING THE TKOF CLRNC. OBVIOUSLY THE TWR CTLR DID NOT OBSERVE US PRIOR TO CLRING THE OTHER ACFT FOR TKOF. ALSO THE GND CTLR DID NOT MONITOR OUR PROGRESS AND COORDINATE WITH THE TWR CTLR. HAD ONE OR THE OTHER CTLR BEEN MONITORING OUR PROGRESS; ONE OR THE OTHER COULD HAVE STOPPED EITHER US OR THE ACFT ON THE TKOF. THE GND CTL SHOULD CHANGE US OVER TO THE TWR FREQ PRIOR TO US CROSSING THE ACTIVE RWY. ALSO; IF THE GND CTL INTENDED FOR US TO HOLD SHORT; SHE SHOULD HAVE CORRECTED US WHEN WE DID NOT READ BACK THE HOLD SHORT CLRNC. SUPPLEMENTAL INFO FROM ACN 636174: I CALLED BFI GND FOR TAXI INSTRUCTIONS AND WAS GIVEN THE FOLLOWING; WHICH I WROTE DOWN AND READ BACK. 'TAXI RWY 13R VIA TXWY A; A7 AND BRAVO. CROSS AT RWY 13L AT TXWY A7'. THERE WAS A SQUEAL FEEDBACK (SIDE TONE) DURING TRANSMISSION AND AFTER THE READBACK. I ASKED GND HOW HE READ THIS TRANSMITTER AND HE REPLIED; 'GOOD; EXCEPT FOR A SLIGHT SQUEAL.'