Thanks for posting your question to the Slingbox Community. You can absolutely view your Slingbox SOLO on a Kindle Fire. If you are having difficulty selecting the correct set-top box during the setup process to ensure your virtual remote is fully functional, here is a wonderful resource.
This is a great article that will allow you to input your Slingbox and set-top box models, and will generate specific setup instructions based on your unique home configuration. Additionally, if you cannot find your specific DTV set-top box model, there is also a DirecTV Universal Remote option within the same tool that should function just fine. Once you have the SOLO completely set up, and configured to your set-top box, you should have no problems whatsoever viewing your TV signal via the Kindle Fire (keep in mind that you do still need to have the SlingPlayer app installed on your Kindle).
Hope you found this information to be helpful!