Shiny Doduo is one the latest shiny Pokemon added to Pokemon GO. As with many shiny Pokemon, finding them is the hardest part, but with all recent shiny additions, Niantic Labs increases the odds of seeing one for a week or two.
The weekly challenges for players can offer a shiny Doduo and players can hatch them in eggs for a short amount of time.
Shiny Doduo Pokemon GO: How to Catch a Shiny Doduo
In order to catch a Shiny Doduo, the most important tool a trainer can have is patience. Doduo itself is a rare Pokemon, spawning less than 1% of the time in the wild in its normal form. With a spawn rate that low, its chances of being a shiny are much, much lower. Once you have a Shiny Doduo, it will take 50 Doduo Candy to evolve it into Dodrio, although it won't help much, as neither Pokemon is super effective in gym battles or player-to-player battles.
The best place to look is parking lots near plenty of PokeStops and Gyms. Those usually have high spawn rate of normal Pokemon like Doduo. The next is to hatch a lot of eggs over the next week or so. Go outside and start walking!