It was a PITA to find because as always the Amazon Prime Video interface is 1000% trash however I can confirm that the Nickelodeon 24x7 TMNT cartoon channel is there. It's currently playing "Venice on the Half Shell".
I learned about it when I subscribed to Amazon Prime Video and learned I can watch all the classic Mario Bros cartoon from the late 80s. Honestly, the whole Prime Video is chaos. Even though I got Prime for free, I would not pay for it.