Can I watch Tennis TV on an Amazon Fire tablet?

Yes, you can watch on an Amazon Fire tablet.

New: there is now a native Amazon Fire Tablet app in the Amazon app store

Alternatively you can access the standard Android app via Google Play.

To do so, you will need to install Google Play and various pieces of Google software onto your tablet. Then download the Tennis TV app from the Google Play store.

This article guides you through the process on how to install the Google Play Store  on the Amazon Fire tablet or the Fire HD 8 tablet.