Although the Kindle Fire runs on the Amazon Appstore, you can still side-load quite a lot of Android Apps, and it requires no rooting. You can side-load apps in all Kindle Fire models, including the latest Kindle Fire HD and Kindle Fire HDX. Below, you can find a complete discussion on how to do it.
Complete discussion on Kindle Fire HDX and side-loading apps:
The Amazon Appstore does have over 100K apps, and you can find most of the apps that are well known in other App stores, like Angry Birds, Minion Rush, Netflix, The Sims Free Play, Pandora, Glow Hockey, Subway Surfers, Temple Run 2, Where’s My Water, Talking Tom Cat 2, Solitaire, Twitter, Minecraft PE, etc. You can always do a search to see if the apps you want are there.
After a long wait, they finally added Candy Crush Saga to the app store for the Kindle Fire and you can now get it directly instead of having to side-load it.
If you still aren’t able to find your favorite app on Kindle Fire, you can try to find and side-load apps from the Google Play store. It’s easy, and no rooting is required; you just have to allow apps from other places in the settings of the device.
Finally, I suggest you read this discussion on Kindle Fire + Google Play store: