I think I may have found my solution. For $4.99/month, I can subscribe to ESPN+. The app lacks the core ESPN channel but subscribers can stream one free NHL game each day for the upcoming regular season. It would be really cool if I could select the game, but I think it's random and I'll be fine with that. Not a bad deal as long as the app works with Amazon Prime/Fire which I believe it does. I still won't be able to watch the core ESPN channel, but I don't care. I'm looking for one NHL game a day and not of any particular team. I follow the league more than I do one particular team.
I love ESPN+. You can also stream every NHL game the next day(atleast they had the playoff games), and they are on there for a while. I'm assuming it would be more of the same this year. I do that at work, duel monitor is amazing. I can put it in a corner spot, and utilize half of the rest of the screen as well as my other screen.
They also have the 30 for 30 shows, and they added in during the NBA Playoffs a special from Kobe Bryant talking about 1 player from a previous game. They have an MLB game per day(looks to be random as well). It really isn't bad for the money you pay. And it will only expand in my view.
Oh, forgot to mention all MLS and ULS games(Phoenix Rising), etc. It's a sweet deal if you like sports.