Though such information may be classified as "good to know", I don't think the manufacturers have a way for this number to be determined. There is no "flash count" value as far as I know. If so concerned, probably best to buy a new set.
if "red-eye mode is activated, is that 1 flash or 4? ?
I've always thought that many are too concerned with shutter counts, but of course it is the one objective measure in the 'age' of an DSLR (apart from actual age, that is)
For flash units, it would be even worse. Would 500 full-power flashes be better or worse than 2000 1/4-power flashes? How many flash activations during the AF-assist? Thank goodness none have a flash counter yet.