Here's why:
* Mudkip is a Hoenn region Pokemon: Mudkip was introduced in Generation III (Ruby, Sapphire, Emerald) and isn't found in the Kanto region, where Pokemon Shiny Gold takes place.
* Shiny Gold is a ROM hack: It's based on Pokemon Gold, so it features the original Kanto Pokemon and doesn't have any new Pokemon added from later generations.
To find a Mudkip, you would need to play a Pokemon game from Generation III or later that includes Hoenn region Pokemon.