I watched the episode where Meowth is telling his story. Aside from that, I read several threads where it was stated that he cannot learn any moves and he might be level 100 but is weak due to not fighting when he should have been.
The question is: how long it did it take him to learn to speak the human language? Is this possible to answer?
As far as I am aware of, there is no evidence on the internet that tells exactly how long it took for Meowth to learn how to talk. But based on the episode (70) as he was learning how to talk, the window showed changes in the season. It changed four times so it can be concluded that it took him at least a year. After he learned how to talk and walk, he went over to the Madonna (the female Meowth that he likes) to tell her that he is now like a human. But Madonna recognizes her straight away. Therefore, it was at least 1 year, but only a bit over a year because she took no time to think about who he was.