Wiktionary
phr. (context idiomatic vulgar followed by a wh-clause English) I don't know; nobody knows; it is unclear.
Usage examples of "fuck knows".
I played stage door Johnny until I got disgusted with myself and she blew town for fuck knows where, leaving me a legacy of soft contralto warbles on hot black wax.
This mission is going to be over in forty-eight hours at the outside, that's the scuttlebutt, but who the fuck knows for sure?
Hinchley's testimony would have dragged you right into the open, along with fuck knows how many of your influential friends.
A psych lead: the killer had just brutally snuffed his victim and transported the body from fuck knows where, yet he still had the calm to coolly dispose of his car _by the dump scene_--which meant that there were probably no witnesses to the snatch.