One of the problems I had with Amazon Instant Video on Android was casting to video to a Google Chromecast Device.
You need to download the Instant Video app which now working officially on Tablets finally ! You can download it from the Amazon App Store.
If you don't have the Amazon App store not to worry , just follow these instructions to install it:
Once the Instant Video app is running and you are logged into your Amazon account you can then cast your screen to the Google Chromecast to watch the videos on the big screen.
The casting of your tablet screen is dependent on your Android version, usually it is Android 4.4.2 and higher. Hope this helps !