Is it possible to make a podcast out of any flash video on the web that I can listen to on my iPod?
One of the reasons content providers choose Flash is that it makes grabbing the video for your own purposes nontrivial. Some sites provide links for downloading video, even if the embedded player is Flash. But I don't think that's what you're asking.
RealPlayer (http://www.real.com/realplayer/download) provides a free player as well as a program that will run in the background to try to grab Flash video. They also have a free converter program (RealPlayer Converter) for transcoding, if what you capture isn't something your iPod can play. If it's an iPod Touch, then you can play H.264/AAC or H.264/MP3 movies directly. Other formats you'd have to convert.
If you are talking an audio iPod, you need to pull the audio out of whatever movie you capture. I would do that using QuickTime 7 Pro, a $29 purchase. There are free alternatives, I'm sure. But taking just the audio from a Flash video is a bit obscure.