Although I've seen some literary magazines asking for short forms, hybrid forms, and innovative forms, I haven't yet seen a magazine asking for strictly flash CNF. I think there's a real interest in having such a publication, and I'd definitely want to publish in one!
For instance, it can be arduous to spend an entire book worth's of time with someone, especially if they aren't incredibly witty, profound, or famous. Flash is a great way to get out some of the memoir-istic anecdotes we have inside of us without alienating, explaining too much, or spiraling into dullness. Likewise, it's a good way to test a topic before committing to writing a longer piece.
I'm thinking about experimenting with this form in my own writing, and also about publishing a modest lit mag that would provide a home for the work, the way that Vine Leaves does for vignettes and various other places do for novellas, or novelettes, or formal poetry. We'll see if that ever happens, of course, but it seems like a good idea to distinguish a market through specialization since there are so many lit mags out there.