AllCast is a great app for sending local and DLNA content to a Chromecast, DLNA, Apple TV and the app recently added Amazon Fire TV support. The app has just been updated this time adding Google Drive support, so you can stream content stored on your Google Drive to any of the supported devices.
There is a trial version that has a 1 minute viewing limit so you can give it a try and the full version costs £3.05 from the Google Play Store.
BETA: Amazon Fire TV support
BETA: Google Drive
Potential fix for disconnecting after 30+ minutes
Various bug fixes