I personally use Amazon Fire TV and the Amazon Fire Stick and it works well connected with my Galaxy S3 and Galaxy Tab 4. The Microsoft Wireless Display Adapter is supposed to work with Android devices as well.
How to use display mirroring on the Fire TV and Stick (from Amazon's website):
To quickly start display mirroring, on your Amazon Fire TV remote
press and hold the Home button and select Mirroring. Then connect your
compatible device. Swipe down from the top of the screen to open Quick
Settings, and then tap Settings. Tap Display & Sounds, and then tap
Also note that Chromecast doesn't stream everything from the device. It streams from the Chrome browser and select apps. Miracast enabled devices, like the Fire Stick, stream any video and audio that is on the mobile device screen (with a slight delay, of course).
Hope this helps!