For the latest 'how-to' on posting images to FlyerTalk, please refer to the wiki on the Travel Photography forum for the best and most up to date information on this:
How (and where) to embed your pictures in the Travel Photography forum
To embed video in your trip report, simply paste in the URL (from Youtube or Vimeo) in the normal way. There's no need to use any code, the URL on it's own will do.
The video will be embedded when the post is submitted. Note that it doesn't show when previewing the post.