When encountering a wild Pokémon, you have a 1/8192 chance to encounter a shiny Pokémon in the wild.
With the odds essentially being a 0.012% chance I would go months without finding a shiny, but I was once lucky enough to find two in a short period of time.
I have played a majority of the Pokémon Games, starting with Red/Blue/Yellow up until Alpha Sapphire being the latest I have played, but there is one thing I have never encountered before: An NPC with a shiny Pokémon.
Is it possible for an NPC Trainer, such as a Gym Leader or the Elite 4, to have a shiny Pokémon? If so, would the odds still be 1/8192 or are the odds different?
If you mean a random shiny then no, NPC trainers always have predefined Pokemon.
The only case I’ve battled shinies was at the Trainer Tower in Pokemon FireRed/LeafGreen.
The Trainer Tower has three Trainers who use Shiny Pokémon: Burglar Jac has a Meowth, Twins Jen and Kira have an Espeon, and Fisherman Kaden has a Seaking.
In the Single Battle mode, the seventh Trainer has a Shiny Meowth, while in Double Battle mode, the first pair of Trainers have a Shiny Espeon. Finally, in the knockout mode, the fourth Trainer will send out a Shiny Seaking.
Here‘s also a video proof of shiny Espeon.