Welcome to the forum!

From the link you posted, it appears that the choices in Armstrong are either modern or ancient. It makes absolutely no difference which one you use. They are the same thing, just in different hues. Pick the one you like the best. I personally prefer the "ancient" colours, as they tend to look more lively and quaint, where "modern" colours seem to be very dark. But it's absolutely your choice.

As for flashes, red is the standard. You can never go wrong with red. And since your tartan has a bit of red in it, using red flashes will look that much better. If it were me, though, I would choose traditional wool garter ties instead. They look much more suave than the cookie-cutter flashes. Little details like this can make a big difference in the overall effect.

But no, they needn't necessarily match the tartan. In fact, they needn't match anything at all. They can stand on their own, as it were. Just make sure the left one matches the right one and you'll be fine.

As for hose, I think you'll find that most people nowadays advise against white. There was a period of a couple of decades where white was popular, but it's really not traditional, and the visual effect is nowhere near as nice as wearing coloured hose. Or better yet, if this is a formal affair, wearing patterned (diced, Argyll, etc.) hose.

I see that you're in England, so I shan't comment on which jacket, shirt, and tie would be most appropriate, since I'm unfamiliar with the traditions of formality for a prom there. In fact, I didn't know they did proms in England!

What is the stated dress code for this event? Is it "black tie", etc.?