Is Aerys II based on King John of England?

No, not at all. King John was a lot of things, but he was not insane or particularly murderous. If King John has a parallel in ASOIAF, I’d say he’d be a lot closer to Aenys. 

Aerys II reminds me a lot more of Ivan the Terrible, if Ivan’s competency in government and war was given to Tywin and Aerys only got the paranoia, the murderous rage, and the sadism.