To begin with, you will need to download the Youtube video that you want. There are a number of ways in which you can do this. The most popular ones are to use the online service Vixy. there are also a number of diffrwent Firefox addons that you can use to download the video of your choice. a few of my favriout addons to do this are either Fast Video Downloader", or VidoDownloader

If you are not a fan of Firefox, then you can always use this handy little program called Youtube-dl. To install this, run the following command:

sudo apt-get install youtube-dl

Then to download the video that you need:

youtube-dl http://YOUTUBE_VIDEO-URL

Now that you have your Youtube video downloaded, you can now convert it.
To do this, you will need the ffmpeg package installed:

sudo apt-get install ffmpeg

To convert your flash file, you will need to do something like this:

ffmpeg -i FlashVideo.flv -ab 56 -ar 22050 -b 500 -s 320x240 FlashVideo.mpg

So what does all this mean?
The FlashVideo.flv is the name of your flash file.
-b : video bit rate. The default bit rate is 200. So you will only need to include this if you want a different bit rate
-ab : audio bit rate. the default is 64
-ar : sample rate. This default for this is 44100 Hz
-s : Frame Size. the format of this is Width x Height. The default is set to 160x128

This can be used for Youtube, Google Videos, and many of the other popular video hosting sites (as long as the format is .flv)