No there are no monthly fees associated with the Amazon Fire Stick.
You can buy the Amazon Fire Stick and watch some free tv shows and movies through the Amazon Fire Stick using your Amazon Prime Membership.
However if you want to watch some of the other Channels and Streaming services then you pay a monthly fee for those streaming services.
The monthly fee for those streaming services is paid separately to places such as Netflix Hulu and many other streaming services that are on the Amazon Fire Stick.
Just like the Roku you do not have to pay a monthly fee to use it unless you want to watch those paid streaming services.
It's well worth the cost to pay the small monthly fees to watch several movies and shows that can be streamed on either the Amazon Fire Stick or Roku device.
But after you buy the Amazon Fire Stick you don't have to pay a monthly fee.