Well, I was searching for a Magnemite that was holding a Metal Coat, and I ran into a shiny one! I named it Rhodium and as I was training it in Melemele Sea, I came across a shiny Luvdisc, which I named Yellow Tang!
Wow what luck!
I just chained my first shiny. Little Pikipek, chain of 94 on route 1. I love shiny Toucannon. My Smeargle was only level 31 so I didn't have too many options in regards to Pokemon, but I think I might try for Eevee next.