Shiny Doduo is coming to Pokemon GO as part of the Mega Evolution themed events that will be occurring all September. Shiny Doduo will become available starting September during Mega Buddy Week. During this week Doduo will be more frequently found in raids and in the wild so it's the perfect time to go looking for a shiny.
Shiny Doduo Pokemon GO: How to Catch
Shiny Dodou can be easily differentiated from its standard counterpart by its lime green color pallet. Its evolved form Dodrio is much the same aside from some bright pink tail feathers, making it look kind of like a three-headed, flightless, Xatu.
To maximize your chances, try looking for Doduo in raids. Pokemon found in raids have a higher chance of being shiny than those in the wild. Try to be out and about in windy and partly cloudy weather as well, Flying and Normal types respectively spawn at higher rates during those weather conditions. Between Sept. 22-28 there will also be higher spawn rates in the wild as a result of Mega Buddy week.
Mega Buddy Week will also have a bunch of passive effects on things like Poffin duration and Mega Evolution duration.