I have a couple of fire sticks. They all have the ESPN app. With the ESPN app, I am able to stream any game that is playing live (or play it afterwards) from inside the ESPN app. I don't know if you can access the ACCN live if there is not a game going on (their pregame shows, the Packer and Durham talk show, etc). But you should definitely be able to watch games that are televised on the ACCN.
There might be a few cable providers left where you can't stream ACCN or ACCN extra content but it looks to me as though that has either all gone away or is about to go away.
I think there were a few initial agreements with providers where you could only watch the ACCN linear channel but they are going away as the 'real' agreements get fleshed out and signed.
If I am wrong, someone please correct me.