Twitter flash images basically serve the same purpose as the Static Images do, people can click on them to go to your Twitter Profile and follow your tweets about the world. The flash based images are however the "pimped out" versions (for lack of a better description) of the static images and offer many more bells and whistles as they are animated which means the possibilities are endless and include everything from flying Twitter birds to bouncing "t's" and more.
These are definitely the most attractive image applications to have on your site and are most likely to attract visitor attention from the start.
On Twitterflash.net you will find a number of these applications which can be personalised by typing your own name into the string of code that needs to be placed into your website's coding, the result? A Twitter image that says for example "Follow Jane on Twitter" with your name inserted into it rather than the generic "Follow me" that everyone has (although we have those too if you'd prefer).
Another great thing to look into if you have a website of your own, is the Twitter Widget application, click here to read more.