It works with the Dish Remote Access app on Android Market. I've used it, it works great, same for iPad.
https://market.android.com/details?...sMSwxLDEsImNvbS5zbS5TbGluZ0d1aWRlLkRpc2giXQ..
Most all streaming sites intentionally do NOT work with tablet, or smartphone browsers.
As far as the Kindle Fire it might, however, Fire limits you to Amazon's Appstore, which doesn't have Dish Remote Access. If you can get the .apk (kind of like the android version of a windows .exe) you could possibly install it directly to your tablet (called sideloading)
You'll probably be better of on finding instruction on how to sideload the Android Market app, im sure you can get DRA app at that point. You can also install a custom ROM that would include Android Market in it, but that is getting even more complicated.