no...but there's no reason you can't enter fan fiction in the short story or flash if it fits the theme
I got into writing in part due to fanfiction, so I consider it a valid form of writing. A lot of classics are also, at least technically, fanfiction. The Odessey, for example, is technically a collection of oral history and other writings. So give it a shot!
I very nearly submitted a Batman (Adam West series) fan fic into this month’s flash competition. I scrapped it because the ending wasn’t up to par but now it’s in my head and won’t go away. It’s gonna happen though, some bat-day, some bat-channel.