Update: The issue was fixed after about two days.
I just got off the phone with customer service from Amazon. I normally spend my workday listening to tunes that I stream from Amazon music on my Kindle Fire tablet. Today, I wasn’t able to stream. After completing the usual round of troubleshooting, I contacted Amazon Customer Service.
The helpful rep informed me that music streaming was down for Kindle users like myself due to a problem with a software update that makes it impossible for the Kindle to access the server with the music. Amazon music was working on my phone and the rep said it’s working on Echo devices as well.
She assured me they are working on the situation. So, if you’re not able to listen to music on your Kindle tablet, you are not alone. I’ll let you know when I hear more about the issue.