It's really a stretch to call 'Girl, Interrupted' 'kind of a funny story'. However, if we look closely, some of the characters' idiosyncrasies and their attempts to cope with their situations might seem oddly humorous. But this is just a very minor aspect. The movie is mainly about the harsh reality of mental illness, the stigma, and the journey of self - discovery. So while there might be a glimmer of what could be construed as 'funny', it's not a characteristic that defines the story.
I don't really see it as that funny. Maybe there are some moments of black humor, like the absurdities of the institution's rules or the strange interactions between the patients. But overall, it's a serious movie about mental illness.