Hi Pat,
The only way to install the aRFR on the Kindle Fire right now is to root the Kindle. Instructions for doing this are available via a Google search- it is pretty easy to do. Just be aware that some Amazon apps will not work while the Kindle is rooted and that rooting your Kindle may void your warranty with Amazon.
Once the Kindle is rooted, you can install the Google Market (now called Google Play or something like that), which will allow you to install the aRFR. Simply "side loading" the .apk file by copying it from your phone to the Kindle without installing Google Market will not allow the app to authenticate, so it won't be activated.
If you sign in to the Google Market on the Kindle with the same account as on your phone, it will recognize that you have already purchased the app and activate it for full use.
If you are planning to use the Kindle as a "shop tool" or it will be out of your control at times, then I would create another Google Market account for it so that people with access to the Kindle can't purchase things using your account info. Of course, you would then need to purchase the app using the "shop" account to get it to work.
Hope that helps-
-Todd
www.etcconnect.com