In the episode Island of the Giant Pokemon, Ekans and Koffing give a speech about Pokemon not being bad, but rather obeying bad masters. Meowth responds saying his master is never around and he still does bad things, implying that Meowth is not owned by Jesse or James. Do we know who his trainer/master is?
Not sure if it counts as an answer, so posting as a comment. According to bulbapedia, this might be a plot hole caused by original Japanese script having a dual meaning - "One implies that he has a master, and one states that he doesn't have a master"– WondercricketAug 24, 2022 at 17:33
2Whenever I watched that episode I always assumed that Meowth was referring to Giovanni. Giovanni, of course, somewhat rejects Meowth in favour of Persian, but I was under the impression that Meowth still viewed Giovanni as being his master, even if he didn't technically belong to him.– ShowsniAug 26, 2022 at 21:38
In the anime, Team Rocket's Meowth is technically a wild Pokémon. Which is to say he isn't bound to a Pokeball and thereby has no trainer.
The strongest evidence of this is during the Black & White series when Iris and Cliff try to catch Meowth at various times with a Pokeball. Meowth actually gets sucked into the Pokeball but breaks out before being properly captured each time. In the anime, when you try to catch a Pokémon that already has a trainer, the ball is shown to simply not work, it bounces off without opening or sucking the Pokémon in. This has something to do with some kind of tagging system which I don't think is ever explained in detail but for the most part Pokeballs somehow "know" if a Pokémon is already bound to a Pokeball so that you can't arbitrarily catch other people's Pokémon. Therefore, since Pokeballs are working on Meowth he is not already bound to one and thus does not have a trainer. He hangs out with the Team Rocket crew by choice, not because any of them own him.
I'm not sure about the Pokeball thing. The earlier episode where Ash gets Charmander, it does get sucked into the ball before popping out once. Aug 25, 2022 at 14:51
The answer will be none.
Meowth's whole backstory has been shown in multiple flashbacks in the show and his whole journey was without a trainer (unless they retcon it in the future.
In a flashback in Go West Young Meowth, Meowth's earliest memory is being alone at Camp Pokéhearst without food and trying to eat a basketball basket. There only he watches a movie called That Darn Meowth! which inspired him to go to Hollywood which he believed would be a paradise. But he was treated as a stray there and later taken under a Meowth gang, led by a Persian. There only he saw his crush Meowzie. But she rejects him for human and he tries to be like humans by changing his walk and learning the human language but got rejected for being a freak. Heartbroken, Meowth remembered the first human word he understood—"rocket"—and was inspired to join Team Rocket.
In Battle Aboard the St. Anne he referred to himself as Top Cat of Giovani before Persian. But in Training Daze, he was at Team Rocket HQ with Persian already being there. And Meowth became a servant to Giovanni, bringing him food and drinks unsuccessfully. Giovanni didn't appear to be angry, but he assigned Meowth to Jessie and James's team.
Covered in more detail on Bulbapedia.