Add Music Files to Your Kindle.

There is one more way of getting your music files on the Kindle Fire tablet, i.e., by making use of Amazon’s Cloud Player tool, which is a tool that comes free with Amazon account. You can store audio files in the cloud instead of the tablet.
Now, you can go to the Cloud player website by making use of your PC and sign into your Amazon account using the right details. When your Kindle Fire device is connected to the PC, it is going to import all your music files automatically.

Kindle Support | Kindle Help | Amazon Kindle Support