Easy. Drag the FLV Playback component to the stage. Don't enter a source, but do give the component an instance name.
Then, just do myComponent.play(shuffledFiles[0]);
More info on the FLV component:
http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/fl/video...
Kind regards,
Pieter
General notice: from now on, I would like to ask everyone to put [AS2] or [AS3] (corresponding to the version of actionscript you are using on your project) in front of their post titles when the question is actionscript related! Please help us help you faster. Thank you. 
