The fastest leaf shutters in general use are cock-and-shoot size #00 and #0 (Compur/Copal standard). They will sync with flash at nominal 1/500, actual somewhat slower.
The fastest sync speed for focal plane shutters in general use is, if what I know isn't too far out of date, 1/250. There are a few dedicated flashes -- Olympus made at least one -- that sync with higher shutter speeds by firing repeatedly as the focal plane shutter traverses the film, but I don't think that's what's wanted here.