Developer Niantic Labs recently introduced Shiny Magikarp and Shiny Gyarados during the Water Festival Event in Pokemon GO. Trainers have discovered the said Pokemon after a couple of hours into the event, but they are not worth the effort in this AR game.
A Shiny Pokemon, like in most Pokemon games, have a different colored model than what they originally have. Aside from the recolor, they bring nothing at all on the table, not even bonus stats.
Shiny Pokemon have the same moves as a normal Pokemon and the other difference they have is the encounter rate. The odds of encountering a Shiny Pokemon in the original Pokemon games were 1:8192, but was later changed into 1:4096.
Shiny State Passes on to Evolution
Spending time walking around just to locate a Shiny is not that worth it since it will not assure trainers that they would have a high IV and a good move set. One would prefer a perfect IV Magikarp than a Shiny Pokemon with lower IV since it can do better in battles.
If the perfect IV Magikarp evolves into a Gyarados, it will carry out the same IV and can even have a good move set. The same goes with the Shiny Magikarp without the perfect IV. Trainers can calculate the IV of a Pokemon with the use of an IV Calculator.
So far, the battle system in Pokemon GO only involves the Pokemon Gyms. What determines the battle are the CP of the Pokemon, its stats, its Individual Values, its type, its move set, and the ability of the trainer to dodge attacks.
Shiny Pokemon will not help in determining the outcome of battles unless developers decide to give them bonus stats. However, if trainers would encounter a Shiny Pokemon without looking for one, that is considered as extreme luck.
Reason for Catching Shiny Pokemon
Most trainers try to catch a Shiny Pokemon for collection, bragging rights, or just simply because of the color preference. As of now, trainers can only show off their Shiny Pokemon by assigning them into Pokemon Gyms they currently have. If developers would release either Pokemon battles between trainers or Pokemon trading, Shiny Pokemon would have some worth.
However, Shiny Pokemon do not work the same like normal Pokemon in the map. If one trainer encounters a Shiny Pokemon on their mobile devices, others cannot see the same Shiny variant. Developers might implement the same system if they would release more Shiny Pokemon and, possibly, legendary Pokemon in the future.