There's a comprehensive choice of browsers (http://en.wikipedia.org/wiki/List_of_web_browsers). I picked one that I knew I wouldn't need and dedicated it to my facebook usage.
I use it to separate my various different Google identities and logins (so I can stay logged in with distinct accounts).
(Google's multiple sign-in is rarely effective or convenient)
Not flash "cookies". You only have one flash plugin that runs in every browser, and has one "cookie" store.
(Not that I know if/whether FB abuses this, I don't even have an FB account. Just sayin'.)