I can't find Ingress in Amazon Appstore, and searching via Google only turned up ways to install it from Google Play Store. There were several questions about how to play it on Kindle on various forums; none of the ones I've checked came up with anything.
Can I play Ingress having only a Kindle Fire as a mobile device?
Ingress can't be officially installed on Kindle Fire. Play Store won't allow you to install Ingress on Kindle Fire. There are some unofficial solutions but you would surely violate the TOS by applying them. You shouldn't do it.
The bottom line is: No.
Either you get the Ingress app the official way (via the Play Store), or you don't play Ingress.
You might manage to install the app some other way. The problem is that the app will notice that. It will tell the server. You will get banned from playing.
You can install the apk Package directly. Before you have to install Google Account Manager, Google Play Services, Google Service Framework and Gmail. Login to Gmail with your Google Account. After that start Ingress. get further information here:
http://www.gizmag.com/how-to-install-google-apps-kindle-fire-hd-hdx/30736/
