How to stop my Facebook messages from coming up on my Kindle?

The only reason why I signed up for Messenger is because Facebook wouldn't let me see or send messages unless I did. When I did that, the only access to the internet we had at the time was our kindle. Now we have an actual computer, but my Facebook messages still come up on the kindle without me being logged into Facebook.

Is there any way I can stop the chat heads from popping up on the kindle? It's really annoying when I'm doing whatever on the kindle and then up comes a chat head that won't go away unless I shut down the kindle and then turn it back on. I also don't like how anyone in my family (or anyone else using the kindle, for that matter) can see my messages. So is there any way to stop it?

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