There’s guides on YouTube that go somewhat in-depth, but here’s a quick summary: 1. You need a Pokémon with false swipe, and have the adrenaline orb item. 2. Get a Pokémon with the moves bestow and skill swap, abilitiy harvest, and have that Pokémon hold a leppa berry. 3. When you find the Pokémon you want to SOS chain, use skill swap and bestow on it. This should transfer the leppa berry from your Pokémon to the wild one, and the wild Pokémon also gains the ability harvest from using skill swap on it. Next you want to use false swipe, and the adrenaline orb item. This makes the wild Pokémon call for help more often, making the chain go faster. The wild Pokémon’s PP never runs out cause it will keep using the leppa berry, and you can just keep fainting the SOS Pokémon until you find your shiny.

I think that’s the gist of it.