Small on-camera flashes that are manually adjustable often have very short exposure times (faster than 1/10000 sec.) and fast recycle times on low power. You could get a bunch of them and figure out a switching system to fire them in sequence.

In general, the lower the power the shorter the time. One method for photographing dancers in motion, for instance, when you need both a small aperture to get a whole set in focus and high speed to stop action, is to use high-powered studio strobe packs with many heads on low power, so you get the full output of the pack with the shortest possible flash duration.