I would like to trigger a photography/studio strobe flash based on the flash of an iPhone camera's LED flash. I'm picturing a device that I could attach to the back of the iPhone temporarily when I want the system to work. I would like it to respond in less than 500ms.
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.