Unfortunately, it's not that simple. This specific implementation happens to use flash because it's fast and easy, but there is also a javascript/css based way of doing it:

http://www.lalit.org/lab/javascript-css-font-detect

It looks incredibly delicate, but it seems to work.

Also, I blocked their flash script and reloaded the page; My fingerprint changed, but I was still a unique butterfly. An absence of fonts is also distinguishing characteristic.