I haven't tried the Firestick, but I have loads of experience with Apple TV, Sony and LG DVD's that can also stream, and most recently Roku 3. By far the Roku 3 reigns supreme, followed by Apple TV. Sony and LG DVD player's were weak. I do not stream from campground WiFi, but instead stream from my own media server that is connected to my own WiFi hot spot.
When I have a solid ATT signal, I have used my iPhone as a hot spot, connected an iPad (or three!) to that hot spot, and had some success streaming Netflix and Amazon Video. That isn't as stable, but it can work. Interestingly, the Amazon app for streaming works much better than Hulu or Netflix for me.
Our kids are 11 & 14, and at that age, it turns out that solid internet is more important than cable or satellite TV. We don't have cable or satellite at home now either--just good internet. I have my sites on upgrading our capabilities to get better WiFi on the coach (5.4gHz instead of 2.5) with a high-end hotspot, but they aren't cheap so I'm not there yet...
If you already have a Firestick, might as well give it a try and let us know what you learn!
2013 Fleetwood Discovery 40G, Cummins ISL,Freightliner Chassis, Allison 3000.
2009 Jeep Wrangler Unlimited Toad w/ Blue Ox Aventa tow bar and M&G Braking System