What happens when you click the link. Do you get an error?
When the Apple TV app is open and active, use a web browser somewhere else on your home network to navigate to: http://<IP_ADDRESS_OF_ATV>:57000/speedtest.
I don't have an Apple TV, but this is how I understand it works.
Load the Test Flight app on your Apple TV.
Using an iOS device (iPhone/iPad) signed in with the same Apple ID as your Apple TV you click the link which authorizes your Apple ID.
Go back to your Apple TV and open the Test Flight app.
The Channels Beta app should be in there.