I haven't decided on what moves my Pokémon can do, I usually check Bulbapedia and check all the generations and take my inpsiration from there. I should write down a list once.
I know Anthony is still very limited in what he can do, whereas Lytse knows a lot of moves that belong to a Cyndaquil beyond its evolution level, like flamethrower (although the anime never cared much about the levels I think, because both Ash's Charmandar and Cyndaquil could do flamethrower before evolving)

And Andy's Pokémon are all high levelled, they have been in the running for 30 years or so, so they know a lot of moves. Which is why he likes to call his Butterfree in a battle against a cocky rookie trainer with a firetype, let them have a laugh at a weak bug and then blast them away with a powerful move >:) Of course he only does that to be educational, you know, he doesn't get any satisfaction from it [s](or maybe a just a little bit)[/s]