The Slingbox M1 can not be setup through the Kindle Application at this time, but after setting this up through a computer through the Desktop Player, you will be able to stream through that application. You can download the Desktop Player and follow the steps in the linked articles below to complete this process:
If you would prefer to complete the setup process on another mobile device, you can use any of the devices listed in this article:
I hope this helps!
Sling Media Technical Support