I've been really wanting to see the TV series, but I have a Roku (no Amazon app) for streaming and I refuse to buy another device for that purpose.
Hunh? One of the benefits of Roku is it is "content provider neutral"! ... A search in Roku will let you know where you can see a movie for free (if available for free), while a Fire Stick will route you to Amazon's $2-3 rental (unless Fire Stick has changed)!
You need to have Amazon Prime to get the subscription as a benefit (I don't think you can get the channel by itself for less), but you do not need another device.
Go to the main Roku menu (cursor to the left all of the way).
Select "Streaming Channels"
Select "Search Channels"
Enter "prime", and "Prime Video" should pop up and you are good to go!
The only way I can imagine you missed this is if you searched for Amazon (I think the official name used to be Amazon Prime, but they changed it to "Prime Video"!
My Roku is about 2.5 years old, but the previous one was around 3 years old when I upgraded. I think access to prime via Roku has been available since prime started, but my memory sucks such that I will not say it was around before I got the Roku ~5.5 years ago. I doubt access to Prime would be dependent on what generation Roku you have as they are always adding and eliminating (when they are go belly up) channels via software/firmware!