I would hope that everyone in the UK knows about the Battle of Hastings, though I'm sure that the SNP won't let anyone in Scotland forget about Bannockburn. (Forgetting about Flodden is perfectly fine though!)
Flodden is pretty well known in Scotland, probably more so than any other Scottish battle after Bannockburn, Culloden and perhaps Stirling Bridge or Falkirk. It's only the English who seem to think the Scots have forgotten, which is strange, because they've apparently taken the trouble to remember a battle that is, in terms of their own history, of no particular significant, but don't regard the Scots as capable of remembering the single most important event in their 16th century.
So, yeah, you're looking at Bannockburn, the great romantic victory, Culloden, the great romantic defeat, Stirling Bridge and Falkirk, which we've sort of blurred together into a single victorious defeat (the Wallace mythos being what it is), Flodden, the second, not-so-romantic defeat and Prestonpan, the second, not-so-romantic victory. You've also got what were technically British battles at which Scots played an important or at least dramatic role, mostly Waterloo, Balaclava and the standard run of First and Second World War battles, which tended to members of every British nationality.