Do I need an app to use it onthe kindle fire...or is it just plain impossible?

I have a tablet and I've been unable to sign on, because my tablet doesn't support Java. It might be the same on your end.

Since the kindle fire seems to have the same apps as the android, i'd suggest AndChat.

Yeah, the site's IRC client needs installed Java, as opposed to the browser's JavaScript. Which means you need a dedicated IRC App.

Seeing how your kindle uses Android I'd simply suggest looking through the google store and then pick one, I personally like AndroIRC.