My kid re-activated prime on me a long time ago, before I had even started thinking about parental controls, by selecting a movie on the Kindle Fire playing with the remote.
Thought I'd learned my lesson, but no. Couple years later he reactivated Audible by asking the thermostat to read him a story. He was probably like 4 or 5 by then. Not only reactivated Audible, but wasted a credit on The Three Little Pigs
My 2 year old reactivated prime twice now, and a britbox subscription, all playing with the remote. I swear you can sit on the fire stick remote and it'll sign you up.
I actually was a prime member the first time, I cancelled it after that britbox subscription. We literally go out of our way now to avoid Amazon--- which is haaaard. At least you can get a refund if you bug them enough.