May 18, 2006 - Closing Down the Flex/Flash Player and Browser
How to shutdown your Flex app completely

From Bill Sahlas:

   private function closeApp():void
   {
       var urlString:String = "javascript:self.close()";
       var request:URLRequest = new URLRequest(urlString);
       navigateToURL(request, "_self");
   }
   <mx:LinkButton id="CloseApp" label="Close Application" click="closeApp();"/>

Or (gets rid of warning prompt):

                                    private function closeApp():void
                                    {
                                                var urlString:String = "javascript:window.opener = self; self.close();";
                                                var request:URLRequest = new URLRequest(urlString);
                                                navigateToURL(request, "_self");                                                
                                    }