There are no evidence that shiny hunting requires you to beat the Elite Four.
According to this Reddit:
These are just some tips from my own experience on how to chain and get yourself a shiny. This is just what I've learned by catching a few shinies myself using this method.
What will help:
- A pokemon with Sweet Scent move (to rapidly increase your search level for that pokemon)
- A high search level
- A large patch of grass (if this is where you'll be doing your chaining)
The only thing that can actually increase the chance of finding a shiny is having the Shiny Charm, which you can get from Professor Birch after obtaining all Pokémon in the National Pokédex.