Yes, you can. You would first need to download the WWE Network app from the App store. Here are the detailed instructions from WWE:
To use your Kindle Fire with your WWE Network subscription, download the free WWE app from the Amazon Appstore.
- Go to the Amazon Appstore.
- Search for WWE.
- Choose the WWE app.
- Click the Get now with 1-Click button making sure your Kindle Fire is the selected device.
If you are a subscriber:
- Open the WWE app
- Click on WWE Network.
- Sign in to your WWE account.
- Enter the Email address and Password for your WWE account.
- Select Log In to sign in.
- Once your account has been verified, you will be taken to the home screen and can select the programming from WWE Network that you want to watch.