Short answer: Because I'm a geek.
As far as I know, there is no formal definition of "flash fiction" (probably because there isn't much money in it, but that's another discussion). Most publishers want short fiction that's at least 2,000 words long. The flash fiction sites I've seen define it as pieces of fewer than 1,000 words, or fewer than 500 words.
(Aside: Yes, "fewer" is grammatically correct. All those "10 items or less" supermarket checkout signs? WRONG.)
Those limits have always seemed rather arbitrary to me. I can understand needing to define novella vs. novelette lengths, when there's a difference of tens of thousands of words, but to me, picking 1,000 instead of 900 or 1,100 feels oddly hidebound--choosing a number which seems "round" simply because biology predisposes us to base-ten numbering.
Besides, I like the 500-word range better. It's more concise, which is good for the reader who has not much free time in her busy work day; and it requires me, the writer, to have better focus. But, again, why choose 500? Why not 470 or 608 or 537?
So I choose 512. In binary, 1000000000. Two to the ninth power. Half a kilobyte. It's a computer science thing. It has more meaning to me than the number of fingers I have. If I'm going to pick a number dictated by the nature of the universe, I'm going straight to fundamentals.
Note: I'm still at VP--this post was written last week.