Update (August 2019): an updated guide on install Google Play store and apps from Play Store on Amazon Fire tablet
If you are using an Amazon Fire tablet from 5th gen to the current model (8th gen), it is now easier to install Google Play Store on the Fire tablet.
Please check this updated guide on how to install Google Play Store on Fire tablet.
Update (July 2019): Amazon Prime Video app now supports Chromecast
As explained in this guide, Amazon Prime Video app on Android and IOS now supports Chromecast.
However, the Prime Video app on Fire tablets still does NOT support Chromecast.
Update (2016/02): Android screen mirroring works on Fire tablet 5th generation
For Fire tablet 5th generation ONLY (you can check yours in Settings– Device options–Device model), you can also use screen cast for Chromecast (Android screen mirroring). You can run the Play Store and update Play services. Please follow this guide to run one ADB command.
For all previous generations of Kindle Fire, Kindle Fire HD, and Kindle Fire HDX tablets, you cannot run Google Play store app. Screencast does not work either. If Chromecast does not work after install the 4 APKs, you can … Continue to read the post....