As mentioned on the Kindle manufacturer's website, the browser you're using is experimental and does not have full functionality. It's likely your device does not have the features necessary to use the chat room.
Though the user guide linked above says the browser supports JavaScript (a common cause of compatibility problems), there are no guarantees that it supports libraries like jQuery that the chat room probably uses. If this is indeed the problem, then unfortunately there is nothing you can do or that we can do to fix the problem.
Make sure you double-check that JavaScript is enabled in your browser settings, for the off chance that's the cause of your issue. Entire websites can stop working properly if you don't have JS enabled.
