Can Reshiram be Shiny in Pokémon GO? As of now, Reshiram's Shiny Form is not available in Pokémon GO.
If we look at how Niantic has conducted new Legendary Pokémon introduction in Pokémon GO, Legendary Pokémon don't get their Shiny Forms until a later event from their initial release.
Reshiram will be available to battle in five-star raids from May 26 to June 16. It's counterpart Zekrom will join soon, with Kyurem coming after that. There will also be Raid Hours featuring these Pokémon on Wednesdays during their run in Raids.
Can Reshiram be Shiny in Pokémon GO?
Normally, Legendary Raid Hours have increased Shiny encounter rates, but there is no official confirmation that Shiny versions will appear during these events. It doesn't seem likely we'll find a Shiny Reshiram at this time.
As this will be the first time any of these Legendary Dragons will available in Pokémon GO, Niantic would naturally want to bring attention to the normal forms of the Unova elite before busting out the anticipated Shiny versions.
A Shiny Reshiram has gold bands accenting its white body, and generates purple flames instead of red. Needless to say, it's quite regal and befitting the Vast White Pokémon.