for driving brushless motor u can not use ULN series ICs. it'll give only -ve (GND) supply to the motor it can't give +ve supply. because it has only open collector output. u need full bridge which can give bot +ve and -ve to motor terminal pins.
u can develop ur own 3ph H-bridge using MOSFET or IGBT. or u can go with readymade IC for BLDC driver for low power rating.
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go through this thread. good one.
https://www.edaboard.com/threads/187701/
BLDC motor driver IC:
http://www.ti.com/lit/ds/slvsba5a/slvsba5a.pdf