Full code after the jump.

Flash CS3
PC: \Adobe Flash CS3\en\Configuration\Components\Video\FLVPlaybackAS3.swc

Flash CS4
PC: \Adobe Flash CS4\Common\Configuration\Components\Video\FLVPlaybackAS3.swc

View MXML

<?xml version="1.0" encoding="utf-8"?>
<!-- http://blog.flexexamples.com/2008/12/11/using-the-flash-flvplayback-control-in-flex/ -->
<mx:Application name="FLVPlayback_MXML_test"
        xmlns:mx="http://www.adobe.com/2006/mxml"
        xmlns:video="fl.video.*"
        layout="vertical"
        verticalAlign="middle"
        backgroundColor="white">

    <mx:Script>
        <![CDATA[
            private function flvPlayback_autoLayout(evt:Event):void {
                videoHolder.width = flvPlayback.width;
                videoHolder.height = flvPlayback.height;
                flvPlayback.x = 0;
                flvPlayback.y = 0;
            }
        ]]>
    </mx:Script>

    <video:FLVPlayback id="flvPlayback"
            source="http://www.helpexamples.com/flash/video/caption_video.flv"
            scaleMode="maintainAspectRatio"
            skin="SkinOverPlaySeekMute.swf"
            skinAutoHide="true"
            autoLayout="flvPlayback_autoLayout(event);" />

    <mx:ApplicationControlBar dock="true">
        <mx:Button id="btn"
                label="Play Video"
                click="videoHolder.addChild(flvPlayback);" />
    </mx:ApplicationControlBar>

    <mx:Panel backgroundColor="red">
        <mx:UIComponent id="videoHolder" />
    </mx:Panel>

</mx:Application>