Same issue here.
Fire TV second gen with Slingbox 350.
When choosing "Connect" in the app, it says "connecting..." then "starting..." and the light on my 350 comes on. Then it says "Slingplayer loading" and the light goes off. Finally I get a yellow triangle with the words "Conflict - Another authorized user is viewing this Slingbox. Do you want to disconnect him/her?". There is no other user connected. If I say "Yes" it just loops round the previous screens and straight back to the conflict message.