You can also breed for shiny Pokemon with the Masuda Method or the Shiny Charm for finding wild shinies or breeding them.
The Masuda Method increases the chance of breeding a shiny Pokemon to 3/4096. The key to using the Masuda method is not to breed any two Pokémon, but to breed two Pokémon created in games of different countries.
With the Shiny Charm, the chance of encountering Shiny Pokémon in the wild is changed to 1/2730. The chance of an egg producing a Shiny Pokémon via the Masuda method is changed to 1/1024. You can do this just by having it in your bag. You can get it from Juniper in Nuvema Town after completing the national Pokedex.
Hope I helped! :)