I know that the flat cap was indeed worn with the kilt for a brief period of time during the latter part of the Victorian era and into Edwardian times, but that does not make flat caps with the kilt look any better or traditional.
I'm still puzzled by this. If flat caps were worn in Victorian and Edwardian times, how are they not traditional... as opposed to, say, the modern "day sporran" which is less than a century old in its tradition, but is widely accepted as traditional?

I suppose it could be argued that flat caps were a passing fad with kilted attire, and that because the fad did not survive amongst mainstream kilt wearers, flat caps cannot be considered traditional. But surely they at least can be said to have some historical precedent, such that they could be considered at least mildly appropriate?

Not that I own or wear flat caps, mind; it's purely a rhetorical point. My dearly departed grandfather always wore a flat cap, though he was not a kilt-wearer. So in my mind, flat caps are inherently linked to trousers.