Use Chromecast on the Kindle Fire! No root
Step one: Allow for third party apps in the settings of your kindle fire.
Step two: Download the 1mobilemarket apk and install it on your kindle device.
Here is the apk: http://www.1mobile.com/app/market/?ci…
Step three: Open the 1mobilemarket and search for youtube, play music, chromecast and play movies. Then install each one.
Step four: All done! Open up the chromecast app, sync it with your device and you are ready to go!