Although it is possible to catch a shiny Gible in the wild, it is much easier to breed one. To breed a Gible, two parent Pokémon and access to the day care center are required.
Get the parent Pokémon
To breed a shiny Gible, two parent Pokémon are required to be in the day care center. One of them must be Gible, Gabite or Garchomp, and the other can be any Pokémon with which Gible's evolutionary chain can breed.
Get the eggs
After placing the parents in the day care center, the day care man begins delivering eggs to you. Each of these eggs contains a Gible.
Hatch the eggs
Once you obtain the eggs, you must walk and hatch them. There is only a one in 4,096 chance of an egg hatching a shiny Pokémon, so it takes a while to obtain a shiny Gible. It may be a good idea to use a Masuda Method, in which you breed a pair of parent Pokémon from two different countries. This actually increases the chances for a shiny Pokémon to hatch. The best way to obtain Pokémon from other countries is to trade using a Wi-Fi connection across the world.