There's been a minor update to SlingPlayer for Kindle Fire.
In some cases, in particular the first time you launch SlingPlayer after installing it on your Kindle Fire, you may see a message saying that SlingPlayer isn't compatible with your Kindle Fire device. But then, if you try to launch the app again, it launches and runs normally.
This behavior has been fixed in an update to SlingPlayer for Kindle Fire. Be sure to accept any updates to your SlingPlayer software that your Kindle Fire offers you.