So I looked into this, and the short answer is — the Kindle Paperwhite is just not going to work it for the chat.
Think of the chat like a live TV signal. Your device has to stay constantly connected to keep up with messages coming in. The Kindle wasn't built for that at all — it was built for reading books, so the screen, the browser, and the hardware underneath are all designed around something slow and calm, not something live and constantly updating.
The screen itself is a big problem. That paper-like display Kindles use physically can't refresh fast enough — every new message would cause a visible flash while it redraws. In an active room that's happening nonstop, it would drive you crazy.
On top of that, the browser that comes with it is really outdated, and the chat needs a modern browser to even load the room properly, let alone keep up with real-time messages. And even if those two things weren't issues, the Kindle just doesn't have the power under the hood to run it smoothly — it would be slow, glitchy, or just crash out.
Now, with the new 11.0 update, things actually got faster and better optimized for mobile, but that also means older or weaker devices are going to feel that strain even more than before.
TLDR: The Kindle Paperwhite wasn't built for live chat — the screen, browser, and hardware are all too weak to handle it. Even more so now with the 11.0 update. Grab any basic phone or tablet and you'll be good.