They do use the Three network but only in the UK and not when abroad. I’ve used an IDmobile SIM on my sons phone whilst away in Spain, Italy and Germany and not had any issues streaming in HD (1080p from my home server).
In the UK there’s the odd few places I have seen no coverage, but generally out in the sticks in places like Norfolk and Northern Scotland, but all networks seem poor . My work mobile is on Vodafone, my wife’s on EE and they are no better and very patchy in these areas.
I don’t tend to use it with a Firestick as when we go away we normally rent apartments and villas where Wi-Fi is included.