Can Shadow Pokémon be Shiny in Pokémon Go?

Solution 1:

With the introduction of Team GO Rocket Leaders, Shadow Pokemon have a chance to be Shiny. According to Niantic Support's article on Team GO Rocket Leaders:

Defeating a Leader also allows you to encounter one of their rare Shadow Pokémon, which also has a chance to be a Shiny Pokémon.

Shiny Shadow Pokemon are mentioned specifically from Leaders, not Grunts, which makes sense for the rarity of Shiny Pokemon

Solution 2:

At the time of writing, shiny shadow Pokémon do not exist within Pokémon Go. This is confirmed by multiple threads and discussions on reddit.

When shadow Pokémon first came out, there was a post going around about a shiny shadow Bulbasaur. However, the post ended up being a fake.

Solution 3:

This post is old, but I caught this from classic team rocket.