Flash duration is indeed the - burn time - the flash is on.. This is measured in very, VERY short fractions of a second.
Some electronic flash units can go off in as short as 1/10,000 of a second, others even faster. Speeds for some pro-sumer units can reach speeds of 1/50,000 of a second, able to stop a bullet in mid flight if timing is right. Some, faster yet..
All flashes have a duration they are on. From nothing to full bright to back to nothing. If put on a plot they would look like a bell curve, but some would have more of a bell shape than others, while some would be just a spike.
In the "old days" when actual flash bulbs were used, they had a LONG burn duration, and that was just what they were doing inside that egg shape bulb, burning. The filaments were burning, and at such a slow rate, cameras could use high shutter speeds to help freeze the action because the flash was on so long.
Back then 1/500 (or less) of a second was OK in many cameras to sync the flash to the camera. Today, if your camera can do 1/250th of a second for flash sync, your FAST.. But then again, you have to understand the mechanics of flashes and shutters in cameras, and the timing needed to have them go off at just the right moment.
Today, the electronic flash is so quick it HAS to be timed to a shutter speed where the cameras shutter is wide open. If not, you will see shadows on your images. It's very much like the ignition timing in a cars engine. If too soon, part of your cameras shutter is still in the way as it opens. If too late, the shutter is already closing. Both causing shadows on your image.
Many cameras have curtain shutters, called Focal Plane shutters. These are 2 curtains. Some move sideways, some move up and down.
When you push your shutter button down one curtain starts to move and in such a short moment of time the other curtain starts to move. What you have now is a slit moving across your film or chip in your camera. Only part of your frame is being exposed at any given moment. The whole frame is hardly EVER exposed all at the same moment except when doing slow exposures or them at or under flash sync speed. The entire frame has to be open to light from the lens when your flash goes off to be properly exposed.
Many point n shoot cameras have a Iris like shutter or none at all and it is the chip winking on and off that is taking the picture. Regardless, the light from your flash, the single pulse of light HAS to be timed to go off when the shutter is at it's widest and fully open position.
The multi flashes you see many cameras give is a feeble attempt at red eye reduction. The many quick flashes are to cause the iris of the eyes of the ones being photographed to close down some and reduce red eye. It hardly works, but this is NOT part of the actual picture taking process. These rapid flashes add nothing to the actual light of the exposure and if you watch when of these cameras go off, right after the many rapid flashes there is one single bright flash. THIS is the one taking the picture...
Google - papa flash - or - Harold Eugene "Doc" Edgerton - for it is he who brought the electronic flash as we know it into the world today.
Bob - Tucson