Get yourself a red dragon... if you're very lucky.
Now Pokemon Go has added in the Pokemon from the second generation of creatures (The Gold & Silver Game Boy titles), that gives us access to Shiny Pokemon for the first time, plus some other features such as gender. Pokemon Go hasn't gone all the way with Shiny Pokemon just yet, but you can now get your hands on the most iconic ever shiny Pokemon: Red Gyarados.
This particular shiny variant of this classic dragon-type Pokemon is so popular and well-known because a story encounter in Pokemon Gold, Silver & Crystal on Game Boy gave you a pre-determined chance to catch one. Generally speaking shiny Pokemon have a very rare chance of appearing, and so many older fans have a particular affinity for shiny Gyarados. Plus... red is cool. I mean, look at him.
If you're not aware, Shiny Pokemon are a feature added to later generations of the traditional Pokemon where some Pokemon are unique. They're the same functionally as regular Pokemon, but shinies have a different color which really makes them stand out.
How to get a Red Gyarados in Pokemon Go and how shiny Pokemon work
First thing's first - you should know how to identify a shiny Pokemon. For the purposes of this article about Gyarados in particular, cast your eyes to the image above: there you'll see a regular Magikarp, a Shiny Magikarp and a Shiny Red Gyarados from Left to Right.
The most obvious difference is the color, but there is another handy way to tell if you've got a shiny Pokemon: try trading them to the professor for candy and you'll be given an extra warning if they're shiny. These things are damn rare, after all!
This isn't the only way to tell going forward, either. Data miners at research group The Silph Road have discovered files in the game that point to extra images that'll be layered over your Pokedex to tell you the status, and that inclues a little icon that'll indicate shiny status. That's a handy little bonus, though it's not one that's been added to the game yet. Here's an image of what that'll look like thanks to the Silph Road:
Getting a Red Gyarados via a Golden Magikarp
If you want a Red Gyarados, well... it's not so easy. The thing about Shiny Pokemon is like any Pokemon they're random. Catching a Red Gyarados is actually hugely unlikely - so your better bet is to try catching its less-impressive predecessor Magikarp and then evolve it, since evolutions carry over the shiny characteristic.
That means you're looking for a shiny Magikarp that has a gold color as above. You're likely going to have to grind out a lot of Magikarp catching in order to find a shiny one, but that's a good thing - you're also going to need 400 Magikarp Candy to evolve that bad boy into a Red Gyarados.
The easiest way to find a Shiny Gold Magikarp is to use The Silph Road's amazing Pokemon Go Nest Atlas. This page lets you see where nests are for each Pokemon, as mapped by the players. Nests are places where lots of the same type of Pokemon spawn reliably.
Find yourself a nearby Magikarp nest and be sure to pass by there to catch as many as you can. The chance of catching something shiny is admittedly quite low, but if you're desperate for a red Gyarados grinding it out like this is the only way. When you get lucky and get a gold-colored Magikarp, spend the required candy to evolve it and voila - Red Gyarados is yours. Try not to boast too much.