(Dang, this should have been in support)
I've been having intermittent problems on Kindle Fire HD for several days now. I was unable to re-subscribe after my first 30 day sub expired.
I thought it might be a trouble with my Amazon account so I made sure everything is clear on that end. Today I reinstalled the game from the Amazon store and was able to play one game. When I tried to get into another game I hit subscribe and it returned to the first dogfight menu screen. I hit multiplayer then play and then tried to subscribe again. It went back to the first menu screen again and said that there was a problem accessing the Amazon app store. Then the screen went black. Exited, tried to log in. Black screen again.
Edit: Tried again after writing this. I was able to get to the appstore before it froze. Then appstore did not respond. I had to restart the device.
I can access the game fine on my phone. (just cant see well enough on the small screen with these old eyes.) I can log into the forum from my phone or PC. My Kindle works fine for all other apps.
No Dogfight.
2nd Edit: Restarted the Kindle logged in. Hit subscribe. Went to app purchase. hit subscribe for $1.99. It said I have already subscribed. Now I have access to all maps. 
Got Dogfight back but now I need to go make dinner.
3rd Edit: (Hour later) The game works, tough it sometimes takes several tries to log in. I often have to force close he app. Also the entire device has become glitchy.
4th Edit: (Two hrs later) couldn't log in at all. Some times get all the way to "waiting for available game" then it says "Dogfight not responding: Would you like to close it? Wait/OK" The device seems more glitchy now.
I'm going to remove the app from the device and see if it returns to normal.