Believe it or not, there are a total of 10 moves that Magikarp can learn across the mainline series, including Splash, Tackle, and Flail. Though, half of these are exclusive to Magikarp obtained from events.
During July 1998 in Japan, a Magikarp with Dragon Rage was available through the Tamamushi University campaign that was run in magazines published by Shogakukan. Only 30 players who successfully completed the Professor Exam were selected to receive this Pokémon, as well as a Magikarp card with the same move. As very few of these Pokémon were obtained in Pokémon Red/Green/Blue decades ago, it's unlikely any are still around, and they cannot be transferred out of the Generation I and II games.
There were also two Magikarp with exclusive moves distributed through the Pokémon Center New York Gotta Catch 'Em All Station! in the US for Gold/Silver/Crystal, which were given as eggs with a 15% chance of being shiny. One was given out with Reversal from June 9 to 21, 2002, and another with Bubble from January 24 to 30, 2003. Again, these can't be transferred out of the Gen. II games.
From June 26 to August 31, 2015 in Pokemon Center stores in Japan, a Shiny Magikarp with Celebrate and Happy Hour was distributed in X, Y, Omega Ruby, and Alpha Sapphire from June 26 to August 31, 2015.
Magikarp with Hydro Pump was obtainable through an event in Gen 5, though can also be taught it through TR in Pokémon Sword and Shield. Magikarp can also learn Bounce in games where the Move Tutor for it is available.
TL;DR, on top of Splash, Tackle, and Flail, Magikarp learns Dragon Rage, Reversal, Bubble, Celebrate, and Happy Hour through event, as well as Hydro Pump and Bounce in games where Move Tutors or their TRs are available.
