If you keep a baby flounder, what will you do with it when it outgrows your tank? If you're going to eat it, that's fine, but some people get too attached to their fish to do that. Check fishing regs too; if flounder have a minimum length limit, then being caught with an undersized fish could get you fined.
That said, be aware that there are several flounderlike coastal flatfish species that stay small; hogchokers are one of the best known. The fish you are catching may be one of those species, in which case you could keep some for life in a moderate-sized tank.
I haven't kept flatfish yet, but I've been doing some research on them. It looks like most of them, even the ones that come into estuaries and streams, do best in full marine conditions. What tank size you need depends on the species you have. I'm sure a breeder or other large footprint tank would work well.