[alatar]

А чего там сложного?

protected var file:File;
protected var destination:File;
 
protected function button_clickHandler(event:MouseEvent):void
{
    file = File.applicationDirectory.resolvePath("mysnd.mp3");
    destination = File.applicationDirectory.resolvePath("mysnd.mp3");
    destination.browseForSave("Save As");
    destination.addEventListener(Event.SELECT, selectHandler);
}
 
protected function selectHandler(event:Event):void
{
    var dir:File = event.target as File;
 
    file.copyTo((event.target as File), true);
}