I have the BT TV Sport package which said that the BT TV app extra was included when I took the package on, also shows on the email confirming the package. However, I can only register 2 devices, not 4, when I try to run the BT TV app on my Amazon Firestick it says I need to upgrade to BT TV Extra. Device management shows only two slots, with three and four only available if I upgrade, but I as far as I was aware it was included when I purchased it. The two available slots show a padlock in each but not which devices are actually taking up those slots and will not allow me to delete them on the IOS device. Tried to resolve this with the online chat but they just directed me to the BT Sport app which hasn't resolved the issue.
If you have fibre broadband from BT then you're correct that BT TV App Extra would be included with the Sport subscription on BT TV. Feel free to send me a private message with the BT ID you're using, and I'll check what's gone wrong.
If it's just BT Sport that you're wanting to watch, then we'll be launching the BT Sport app on Amazon Fire TVs and Sticks tomorrow morning, where you'll get a much better experience.