Slingbox has only support if you pay the $30, whether they solve the problem or not. If I didn't already have two slingboxes I would look for another option.
They also don't read this forum or bother to respond to it.
Regarding Fire TV, I bought one to replace one of my 2 Roku 3's because Slingplayer would often say there was another viewer logged in when there wasn't. The Fire TV has worked fine but the remaining Roku 3 still at random says there is another user. (Note, I have two separate slingboxes that I can use separately with two remote TVs)
So, I just bought another Fire TV stick to replace the last Roku, and it doesn't have the same problem, however it just created a new one. I tried the setup option and decided to set up favorites on the channels, and now after trying every possible option I still cannot get out of that menu and even powering off the cable box just brings that up when powering on.
There is a disconnect between the Fire TV control options and what is expected by my cable box and now that one is locked on the "favorites" menu and nothing will exit from it, including trying to do so with another device, like my phone. Maybe Slingbox didn't write the app as they say but one would have thought they would be interested in knowing about a bug, but when calling them they say they are not.