A given trait is adaptive if it helps us (or helped our ancestors) adapt to their environments and have a better chance of living long enough to pass on their genes. Therefore, what you are asking is why people who had flashbulb memories would have a better chance of survival than those who did not.
As you know, flashbulb memories are long-lasting and are triggered by intense emotional events. This sort of capacity could be adaptive because many flashbulb memories might have been triggered by life-threatening experiences. Such experiences would surely trigger very strong emotions and, thereby, flashbulb memories.
Imagine the difference between a person with such memories and one without. The person with such memories would remember what sorts of situations almost got him or her killed and would avoid them. The person without such memories might forget these lethal situations and blunder into them again and again. This second person would be much more likely, over time, to get killed.
It is in this way that such memories could have been an adaptive characteristic as the human mind was evolving.