I have found a solution. What puzzles me is that I would have thought the copying of the 'rock' profile for chromium, as suggested by @Arwen would have had the same result.
If I log in to the new account and launch Chromium from the command line specifying the same user agent as is found in the chrome://version for the rock account then Chromium can play Amazon Prime video.
I will now see if I can work out how to get this to be applied when launching Chromium from the GUI.
Thank you all for your help with this.
If I log in to the new account and launch Chromium from the command line specifying the same user agent as is found in the chrome://version for the rock account then Chromium can play Amazon Prime video.
Code:
chromium-browser --user-agent="Mozilla/5.0 (X11; CrOS armv7l 6946.63.0) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/72.0.3626.121 Safari/537.36"
I will now see if I can work out how to get this to be applied when launching Chromium from the GUI.
Thank you all for your help with this.