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There is a well known undocumented MovieClip method called addFrameScript in AS3 that is helpful when creating flash components for flex using Flash CS3 or higher.

It allows you to call a function when the playhead of the MovieClip timeline enters the specified frame number. In other words, we can call a function in flex from the flash swf file at a certain frame.

 
[Embed(source="../assets/swf/myFlashComponent.swf", symbol="Preloader")]
        private var FlashPreloaderSymbol:Class;
 
private var clip:MovieClip;
 
clip = new FlashPreloaderSymbol();
        addChild(clip);
 
 
private function onFlexInitComplete( event:FlexEvent ):void 
    {
 
        clip.addFrameScript(47, callMyFunction);
 
    }

Format
MovieClip.addFrameScript(frame:uint,notify:Function)

We call the function “callMyFunction” when the playhead in the swf file hits frame 47.

More Resources
Flashguru’s Blog

Flash, Flex 3 AS 3.0, AS 3.2, Flash 9