I've got Gibraltar's flat base cymbal stands and really like 'em. The DW and Gibraltar flat base cymbal stands aren't going to be mistaken for vintage gear, but still seem to have the right vibe for use alongside vintage drums. They're not exactly lightweight, but what weight they do have seems to make 'em more stable. My only complaint is a pretty typical one for flat base stands -- sometimes they're hard to position. A conventional tripod can reach over other stands' legs. Flat base stands generally can't.
If you want something that looks even closer to vintage and you don't need a boom stand, you could opt for Ludwig's flat base stands. They've got a smaller footprint than the DW or Gibraltar stands, so they're not quite as stable, but it makes them a little easier to position while still being reasonably sturdy. They're super light and break down small, so they're easy to travel with. They also have a 6 mm post, so the stand is a good choice to use for vintage cymbals with small holes.
Pearl also makes a flat base stand, their BC100S, but you can reverse the base to turn it into a conventional tripod. I like the idea. Fixes the one complaint I've got with my Gibraltars, or at least gives me a workaround.