I’ve been wondering why Tivo would have an Amazon Instant Video app, but didn’t have a link for Amazon Prime videos? The answer is in the chart below. You have to have a 2014 Tivo model or later. Here’s the link.
The other option is to get a Roku 3 to fill-in as it has a nice Amazon Prime interface. I’ve also ordered the Amazon Fire TV Stick, which I should receive soon which is another way to get Amazon Prime. It doesn’t have ethernet, which I prefer, so I’m hoping the wireless is fast enough.