I saw a list here showing Dewgong with 36 (not including TMs & HMs) but that 36 does include egg moves and I think tutors so that's not what I'm looking for.
Thanks in advance
There are two Pokemon that learn the most moves excluding TM/HM/Move tutor moves and egg moves:
Both learn 20 moves (some are repeated once or twice though) in their entire carrier to level 100!
The correct answer now is Galarian Mr. Mime at 26 moves he can learn without TMs/HMs/TRs or from breeding.