How can I trigger a photography strobe from a iPhone LED flash?
Are you sure about 500 ms.  That would be a very slow shutter speed.  In any case, responding much faster than that is no problem.

Photographic strobes are triggered by a contact closure.  Unfortunately the current and open circuit voltage can vary widely, so it is best to use a relay for the general case.  You could use a transistor, which would trigger faster, if you know something about the strobe you are trying to trigger.

The question then becomes how to trigger a relay from a light flash.  The important characteristic of the trigger flash is that it is a fast pulse event, something that doesn't happen much on otherwise.  I'd probably rig up a photodiode into a transipedance amplifier and look for a pulse.  This can be done by high-pass filtering and thresholding the amplifier output.  When the threshold is detected, turn on the relay for 100 ms or so.  That is much longer than a small relay will take to turn on, and much much longer than the resulting strobe flash.