No you don't need Prime, but you have to create an account before you register.
To buy content and deliver it to your device, you'll need to connect to a wireless network and register your Fire tablet to an Amazon account. Registering also allows you to transfer purchases between devices and Kindle reading apps. To learn more about connecting to a wireless network, go to Connect Wirelessly
Register Your Fire Tablet
- From Home, swipe down from the top of the screen and then tap Settings.
- Tap My Account.
- Tap Register.
- If you already have an Amazon account: Enter your Amazon account information, and then tap Register.
- If you do not have an Amazon account: Tap Create Account, and then follow the instructions to set up a new account.