The Kindle is made by Amazon and so the very first step is to set up some kind of Amazon account, which might just be an active email, and you should not need to put in a credit card. Once the basic set up is done, the next step is to use the SILK browser on the home screen and then follow the instructions below:
How to install Google Play Store on your Kindle Fire Tablet.
STEP 1 – Downloading the Files
Download these files one at a time in the order they are here. The four files work together to allow you to use Gmail, Google Play and all the Google apps which we will need to access the classes.
Tap on the link, scroll down, and tap on “Download APK”.