I did some more digging into the Deep Linking to Amazon FireTV apps and while Deep Linking is mentioned, it appears to not be the same as Deep Linking on most mobile platforms, so that option is out.
I guess the only thing I can really do at this point is ask that Twitch implements a way for the HTML5 Video Embed to detect if the platform it is being run on is the FireTV (via the FireTV WebApp platform and the Amazon HTML5 WebApp Tester application) so that it can properly support the FireTV remote and game controllers for navigation, playback and the ability to click thru the Mature Warning confirmation overlay).
Until that can be implemented, the best I will be able to do with my FireTV app development is pull from the Twitch API our channels Live status, the preview image of the stream, stream information, and then have a page in the app that informs the user that they need to open the Twitch App and navigate to our channel manually.