Yes, I actually made an effort to accurately answer this question. Yes, this is what I do in my spare time. No, I do not have a life.
I have a feeling that nobody actually believes that I genuinely answered this, so I'm gonna briefly outline how I did this. I copied the moveset information from arguably the most fantastic Pokedex resource I have ever seen in the history of ever (click the link and go to the Movesets tab). I copied that spreadsheet into my own Excel document and then mirrored the data in another spreadsheet with the =FIND() function so that each mirrored cell either states a number or an error value, the number stating the position in the text string where the letter 'a' appears and the error value meaning that no 'a' value is present. I had to remove all mention of 'Start' in the spreadsheet and then I removed all cells that have 'ORAS' in them, because those moves could only be learned in ORAS. That being said, this information only refers to the moves that Pokemon learn in Sun and Moon. There's also a lot of double-ups too since some Pokemon can learn a move in multiple different ways... but there's a clear winner so it doesn't matter. I then did the whole thing again with the 'A' value instead, since =FIND() is case-sensitive. Did you understand any of that? I don't speak Excel English that well so forgive me if it's nonsense.
But without further ado, I will announce which Pokemon learns the most amount of moves with the letter 'a' in them! In a landslide, the answer to this question is... Mew!
That's right, a-mazingly, Mew has the chance to learn an a-stonishing 66 moves with the letter 'a' in them. This includes a few moves that are doubled up but that not many. Weavile is our worthy runner-up, who is able to learn 60 moves (although this includes a lot more double-ups than Mew). Third prize goes to Rhyperior's 59 moves.
It's not perfectly accurate but yeah, the answer is basically Mew. If someone dares challenge my intelligence then comment below and I'll just hide this idc.
Hope I helped. :)
Source: Above Link and Excel