I'm a fan of fairy tales, not the overly-tired retellings that pass for fairy tales in YA but actual stories about the strange and the prices it exacts upon it's characters. I have lots of opinions on fairy tales in general but the most pertinent one to this posting is that people simply aren't really making them, I can go an entire year and find only one or two amongst ALL of the media I consume.
I suppose people aren't doing it because it's hard. Fairy tales are full of weird turns and odd twists of logic which is something I'd generally only use to describe the worst books I read these days. I started thinking about all of this when I heard that Edgar Allen Poe wrote what's basically a 1001 Nights fanfic (called The 1002nd Night I believe) where Scheherazade spends her 1002nd night telling her husband strange tales of the modern day, so strange that he executes her for it!
I believe that this would be called "the opposite of a fix-fic".
But following the notion that fairy tales should be strange and unknowable to at least a degree, then yes Flip Flappers is absolutely a fairy tale. I was hesitant to call it one at first (wondering if I was overly influenced by it's cute ending sequence with fairy tale images) but the shifting conflict and worlds of the final few episodes convinced me that, while there's really no other story to compare it to in this regard, Flip Flappers is a strange fairy tale of courage, determination, and love.