I kind of thought the "Flat" bit described a flat expanse of land, but then it didn't seem to make much sense in association with lightning, which strikes high points or the tops of spires, etc. and the other meaning of lightning, to do with speed, doesn't fit either.
The flat is also what horses race over in the UK if they're not steeple-chasers, ie jumping fences and water, so then I went off on to the idea of a horse that went like lightning on the flat, but that's a bit of a stretch too.