Can a B.A.M.S or B.H.M.S doctor become an Astronomer in NASA?

Sure. They'd have to go get a PhD in astronomy or physics (8-12 years of college, unlikely many of the medicine classes would transfer), become a US citizen (NASA hires foreign postdocs for 2 year appointments, but not many foreign astronomers full time) and apply for a job. They don't hire many astronomers, so you'll also need to be at the top of your field and do something very useful for them (not theory).