"Exposing himself" is the old and standard term for that particular behavior. "Whipped it out" wouldn't read very well, "flashed" may have been okay, "displayed the family jewels" might cause confusion. 
As for the female version of the behavior, I don't think there is one. Women, for some biological reason, just aren't prone to giving spontaneous viewings. 
It is legal in Eugene for women to go topless. I don't know how often women take advantage of that liberty.