It's been a few years since TiVo released a limited app for Amazon's Fire TV platform, but as it promised last year, the next-generation platform will reach third-party boxes. Those include not only Fire TV (and Android) but also Roku and eventually Apple TV.
We got a brief demo of the experience on those boxes at TiVo's booth, where it streamed transcoded video from a connected Bolt DVR without issue. If everything goes according to plan, you should see the full app for Fire TV in Q2, followed an app for Roku, and later, perhaps in the fall, access will extend to the Apple TV. Additionally, it's not planning to charge for access to the apps, although TiVo owners will only be able to stream to two third-party devices at once.