I currently have BT Sport via Sky TV but am in the process of cancelling Sky TV. Is it possible to change this to using the app only on something like a Firestick?
No need depending on the price you're currently paying, BT Sport on Sky also includes app access and online player, so you already have what you need.
The BT Sport app is currently £15 so if you're paying more than that you could change subscription, it would come with a new 24 month term or look at BT TV which is also £15 per month, so you still get BT Sport on TV along with Freeview access, the box also supports a range of apps like Netflix, Prime etc