I cannot add to the comments already made which all make good sense. I would only add that it might be best to go to a few meetings with what you have, have some fun and see what results you get. I would also suggest that you go to a few different tracks as you might find that man-made tracks have limited access for the public as the main element of the track is not fenced; unless you can get access to the 'inside track' (requiring the organiser's permission and indemnity insurance etc) you may be disappointed whatever lens you have. Club events can also be similarly restricted (club unable to fence the whole track or marshal the public). Big clubs at Hawkstone Park (Shropshire)or Cadders Hill (Norfolk) and similar have great access and you can get so close that 300mm would be too much for a great shot, so a zoom is adviseable.
For what it is worth, I use a Canon 70-200 F4 (with IS which I do not use it for MX) which is lightning fast and sharp even with my 1.4 extender glued to it - which then loses as stop). I also shoot in manual focus most of the time but that is just my preference. To get to those preferences, I used standard lenses, went to meetings and found out when I missed shots, had the wrong lens on, the camera deciding where to focus when I thought it was focusing elsewhere, out-of-focus shots, depth of field issues, bikes racing that look as though they are standing still, how to cover the lens in wet and muddy conditions (or dust!) with cheap plastic bags, where to stand and how early I might need to get there to do so and which tracks not to bother with (access etc). Grasstrack is a great sport as well and gives you great access but some other photographic issues to overcome.
Why do I think this is worthwhile. If you do buy the 70-200 F2.8 (a magnificent lens it has to be said) and find it does not give you the magnification you require for most of your shots, then why add an extender and reduce it's effectiveness? I do, but MX is not my main subject, more a source of great fun, and I find the lens light and good for what I need. A 'x-300' or 100-400, or a prime might be a better option but you don't want to make this decision having already shelled out for a top lens - unless it doesn't matter of course.
So I would take the kit you have got and have some fun at the events and see what you think and there are always people with gear there that are only to pleased to chat. I used to ride myself (a very long time ago) and often see team managers whose sons, and even grandsons are riding now, it is pretty friendly on the whole. You never know, the answers you come up with might be the best 2.8 lens at 70-200, or something bigger, or you might find that your stock lens does the trick for the events you want to attend. I have used my wife's Canon 450 with the 55-250 and managed some great shots at the right track and distance.
Hope this helps a bit.
PS I don't use flash at these events, although I have seen others use it sometimes. I don't recall it ever being an issue when I was riding but there weren't that many cameras around then; from the side shouldn't be an issue but face-on at close-range is something I wouldn't do.