The Fast Hatch code only puts eggs at "ready to hatch" so when you take a step (or put them in Isle Avue) they hatch.
You can use this code with your eggs to avoid the hassle of hatching them by running around for a few minutes/hours. It doesn't matter if you're Shiny Hunting or Breeding, since the only thing that it modifies is the Egg's hatch status.
However, you are not allowed to use any other code that modifies the Pokémon in the egg (Nature changes, Ability, Shinyness, etc)
Thank you for the question, please tell me if something is unclear in the rules and I will change it ^-^