Move the enterFrame listener into the start and stop functions. You were adding the listener as soon as the program started, you'll want to add it only when you want to play, and remove it when you want it to stop.
Code:
function start_play(e:MouseEvent)
{
arm.gotoAndPlay(2);
arm.addEventListener(Event.ENTER_FRAME, rotatearm);
}
start_btn.addEventListener(MouseEvent.CLICK,start_play);
function stop_play(e:MouseEvent)
{
arm.gotoAndPlay(2);
arm.removeEventListener(Event.ENTER_FRAME, rotatearm);
}
stop_btn.addEventListener(MouseEvent.CLICK,stop_play);
function rotatearm(e:Event):void{
arm.rotation += 1}