FaceTime disconnects when flip

Does this occur as soon as you switch the camera around? What version of iOS do you have on the device? After you have changed the camera, are you trying to close the small menu that shows up allowing you to switch the camera? If so, are you just tapping on the screen, or are you tapping on the X in the red circle in that menu? If you tap on the X, that is how you disconnect the call. I found that I would do that every so often, thinking the X was to close the menu. Otherwise, I'm not aware of any issue like that. You can try force closing FaceTime, then power cycling your phone. If that doesn't help, you can do a force restart of the iPhone, and the last steps would be to create a fresh backup and restore the phone to that backup.

What do you mean by, "flip the screen"? Are you referring to rotating it from portrait to landscape, or something else?