like this onehttp://www.youtube.com/watch?v=8XXfEoDIF0Q?
Take a look at step two on this coil gun instructable:https://www.instructables.com/id/S01NZYFF8Y3W8KK/This is pretty much the same thing as your video. This one will even show you how to wire them together into a bank of them. I have seven wired together in my voil gun, and it charges 11 330v 180uF capacitors (the same ones in the camera) in just a matter of seconds.Hope this helps you.
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The easiest way is take the board from your flash assembly remove the big electrolytic cap and replace it with a red and black lead with clips on the end. Then you can attach you cap to the clips and charge it the way the board was designed to. You could also remove the battery clips and replace them with a 1.5vdc wall wort (no more than 3vdc) and replace the charge button with a momentary on button so it fits in a project box. If you leave the board basically as is you can also use it to discharge caps through the strobe.
if there is mains electricity available it may be a LOT faster (but more dangerous too) to charge right off the mains (thru 4 diodes and incandescent lamp as resistor)
the camera is a cap charger
just swap the cap to another one when you want to charge
connect long wires instead of the cap to make it easy
dont charge low voltage caps and be carefull to not swap + and - cause the cap may explode