Amazon uses their own app store, but Fire tablets are Android at their core, and can just as easily work with the Play Store.

However, Amazon Fire devices have a built-in setting that blocks the download of apps from sources other than the Amazon App Store. Before downloading Google Play, you'll need to disable that setting.

However, you won't find the Play Store app in the Amazon Appstore. Instead, you'll need to download and install some APK files directly onto your Fire tablet.