I think this makes a cute nickname for Felicity, but I would never use it as a full name. Come to think of it, I don't think I would ever use the name Felicity either, it's a bit cheesy and sappy, I suppose, for my tastes. Oh well, I could always use this name for a dog.
It doesn't matter if Flick sounds like a boys name because it is to be used as a nickname, not a full name. I think it is very cute for a little Felicity.