You can get your local channels with the DishAnywhere app installed on your Firestick BUT you need to have Dish at home. However it needs a Sling adapter installed on the home receiver and an internet connection. I have this setup on my old/discontinued Dish VIP222K (works with a VIP722 as well) and it works just fine. Actually it not only allows you to get your local channels but also any other Dish channel you're subscribed to.
I don't know what equipment is required to do this with the current generation of Dish equipment, i.e. the Hopper though.
Obviously you need to have a Dish receiver at home with the Sling adapter or equivalent, have it connected to the Internet and on. In your RV you'll need a way for the Firestick to access the Internet via WiFi. With all that in place you should be all set.
I've used this setup to watch all my local channels and Dish channels in my RV while camped in a friend's backyard in Alaska.
