I'm here to debunk and disappoint many of you.
The chain-fishing shiny method is crap. After rigorous testing, I've come to a solid conclusion.

When the fisherman says that "You can get rare pokemon with consecutive fishing," he doesn't mean shiny.

He means the hardest to catch fish in that area. For example, in the Cyllage City waters, every 7 or 8 catches consistently, a Seadra was caught.

All of the shinies that have been caught here have been coincidental or falsified. The reason they may actually be popping up more often is the rapid rate at which you catch the fish as opposed to the slower rate of walking through grass for things to show up.

Sorry to burst all of your bubbles.