Sounds like the sort of thing that could be done without an Arduino! Would probably be a lot easier without one as well. Essentially you're making a "clapper" circuit, but instead of going from sound to light, you're going the other way around.
Try using your LDR/voltage divider input with a comparator IC like the LM311. Experiment until you get the right reference voltage for it to respond to your flash. You may need a peak detector on the output to hold it for a little while... camera flashes are pretty quick!
Use the output from the comparator as the trigger for an oscillator circuit built around a 555 timer or whatever you have lying around that'll do the job. A square wave of a couple of khz will drive a little piezo buzzer quite happily.