The Shield TV has a feature called Framerate Matching that you can turn on in the settings. Most streaming services and Plex/Kodi will use this feature if necessary. Essentially, when you start playback, it changes the fps settings on the shield's hdmi port temporarily to match the content during playback, then it switches back when you return to the menu. That way a 23.98 source plays at 23.98 (24p) and a 29.97 source plays at 29.97 (30p).
To watch broadcast TV on the Channels app, set your shield's hdmi fps setting to 59.94 and you should be good. Now, on 720P channels I do see some screen tearing and break up sometimes. I'm not sure why this happens but I get it with both the Channels and HDHomeRun apps so it has to be something with the way the signal is being sent from the broadcaster.