I just tested the Shiny Pokemon Egg on Crystal and RNG_Reporter is right on U.S. versions it is only 14% chance of being shiny while in Japanese versions it has a 50% chance of being shiny. It took me only two tries though and I got a shiny Pichu that knows Dizzy Punch from that egg and I'm happy.
All Pokemon from the Odd Egg will know Dizzy Punch.