I'm sure if it was a problem using flash, you would have been told very quickly, or a rider would have complained, and it stopped.
With regard to using tv at 1/250 there are a few ways you can try, and find the one which suits.
You could try manual setting 1/250 and select an aperture you want to use f4 ro what ever, the flash will make the exposure.
Or you could change one of the custom functions (I think cf3) to have the camera always sync to 1/250 when a flash is attached, and use in Av with your aperture choice. Only thing to watch is that is the flash runs outs of omph from a few quick bursts, it does adjust to a no flash longer exposure, so you could end up with a panned shot.
for my main work, which isn't motorsport, I'm always using flash, even during the day. I just use either Av (normaly during the day) and Manual at night, but I vary depending on job type. quite often the flash is set to manual as this helps speed up the cameras reaction. I'll take a few test shots and leave it set. But, it could be VERY different for motorsport. Try and see what the other guys are doing, without ovbiously asking them, as they may not tell you.
when you get comfatable, you could try using 2nd curtian sync.