Can Ingress be played on Kindle Fire?
Solution 1:
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.
Solution 2:
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.