What is the process like to go from Enlisted Air Force to Army Flight Warrant Officer? Do you have to attend Army BCT?

You would have to attend the Army's Warrant Officer Candidate School.

Unless you're security forces or cct/tacp/pj/sere, yes you would go to army basic if selected. Then you would go to wocs. If you are interested, check the W.O. recruiting fb page. They list all the installation briefings there so you can see if there is one near you any time soon.

I can't speak to the proper paperwork, but you will attend WOCS. Just one piece of advice, when the TAC officer tells you to "get in the chair".....do NOT go sit in an available chair.