What is the firing rate of the brain while a human remembers a flash bulb? Or perhaps you mean the experience of a "light-bulb going off in the brain, ah ha!" moment?
In both cases, the answer is: more than zero, (probably) less than a grand mal seizure.
The problem with the question is twofold. First, there is just no way (yet?) to measure the activity of every neuron in a human brain. And given the complexity memory/conscious perception/the brain, it's hard (read: pointless) to even try to come up with a ballpark figure. More importantly, this question ... isn't really the right question to ask in the first place. Important information isn't encoded in the brain as a factor of average firing rate of the entire brain. In my opinion, the only thing the average firing rate of the whole brain might tell you with any degree of specificity is whether you were brain dead or not. Even brain activity during an epileptic seizure is characterized more by an unusual degree of synchrony (neurons firing at the same time), rather than a total increase in the number of neurons firing.
A more meaningful reinterpretation of this question might be:
What is the neural process that underlies an "ah ha!" moment? Or, in other words, what is our brain doing when we leap out of our baths yelling "eureka"?
For insight (heh) into this process, we should turn to Dr. Mark Beeman, a professor at Northwestern University. Dr. Beeman studies the cognition of insight and creativity, and gives a lecture titled, "Where Ideas Come From: The Cognitive and Brain Bases of Eureka! Moments". A lecture that you can watch online.
For a general-readership-friendly profile on Dr. Beeman and his work, check out this New Yorker article.