You can download 1.6.0.7 it from 1Mobile. You may want to grap their Store App while you are there as well.
http://www.1mobile.com/es-file-explorer-70957.html
When downloading Apps outside of the Amazon App Store, you will see a small pop-up in the Notification Area of the Status Bar at the Top of the Fire. If you touch the Notification you will see the download in progress. After the download is complete, touch it to launch the App installation package.