Getjar, probably one of the oldest websites to offer mobile apps have got their own app store for android. Thousands of free (and paid) apps to pick from, and best of all, it is fully compatible with your Kindle Fire, and rooting is not even required.
The getjar app store has a great feature called GetJar Gold Apps, which will allow you to download a selection of paid apps for free during a certain period. somthing that unrooted kindle fire owners will enjoy the most.
To install GetJar on your kindle fire, just enable “Allow installation of applications from unknown sources” under the device tab in your kindle fire settings. Thento m.getjar.com on your kindle fire browser and enter the code 16914.
The apk will be downloaded, install it, then open the app to enjoy your new source of apps for your kindle fire