I'm sorry, but you can't use the Google Play Store on Amazon devices. You have to get all your apps from Amazon's App Store.
Amazon actually puts blocks in their devices to keep them from working with the Play Store. Amazon only wants to allow you to use Amazon's own App Store.
If you search around, there are tutorials that claim to be able to work around this, at least partially. But, they can be tough to do, may not work entirely, may stop working when Amazon releases an update, and can even cause your device to stop functioning at all.
Because of this, Google can't support this.
Also, be VERY careful about anything that tells you to get app APK (install) files from other sources and side-load them. Too many of those sources contain versions of apps that are packed with virus or malware.
For further help with your Kindle, you need to contact Amazon Support directly.