I found the same problem and am looking for a solution too. I started the Peacock app on my LG Smart Tv; was able to log onto the Peacock service, but nothing will actually start. It switches screens as if to begin playing and then goes back to the episode selection page. The TV is hardwired to the cable modem; I can play the episodes on the X1 box using the app. However the LG app does not play it.
I tried removing the power to the X1 box, thinking it may detect the X1 device as an active Peacock screen, but the LG app still fails to play an episode. My iPhone also will connect and play using Xfinity Wifi connection.
moved your reply to a separate thread in the stream app area of the forum.