Actually it's "J'ai fini", the song title has the wrong verb. "Je suis fini" isn't grammatically correct. "Je suis fini" could be used in a conversation and could loosely translate to "I'm dead tired" (but it's almost... slang.) or something like that, but it's not "i am finished". Unless they mean dead tired lol i don't know.
That was my thought too; I guess they wanted to translate ''I'm done'' or something. Fucking Google Translate.