I understand that you want to know if the SlingPlayer for Kindle Fire will work with the Dish Network and the Sling Adapter.
The short answer is no. If you want to use the SlingPlayer for Kindle application, you must own either the Slingbox SOLO or the Slingbox PRO-HD. I encourage you to check the following links in order to get all the information about this application and the required Slingbox models:
Hope this helps!