Shiny Glameow Pokémon GO is available during the Sinnoh Throwback Challenge.
The Sinnoh Throwback Challenge will run from May 22 to May 29, during which you could find Shiny Glameow in the wild.
Shiny Glameow Pokémon GO: How to Catch
The event simply introduces the Shiny form of Glameow, as the encounter rate for it will not be boosted. That means you'll have roughly a one in 450 chance of finding a Shiny Glameow.
Shiny Pokémon don't appear on the map as Shiny, so you'll have to engage each Glameow you see until you find one. Once a Pokémon has been released as a Shiny in Pokémon GO, it will always be available as such going forward. A Shiny Glameow is light purple rather than grey. You'll always get a sparkle to denote if the Pokémon you've encountered is Shiny.
The event will just make Glameow easier to find, as all Pokémon originally from the Sinnoh region will be more common. If you're hunting for a Shiny Glameow, you'll have to do it the old fashioned way. Previously "featured" Shiny Pokémon for the Throwback Challenge also did not receive a boost in encounter rate.
Glameow will evolve into Purugly, who doesn't have a lot going for it in battle. Get a Shinny Glameow for your collection if you like it, but you won't need to seek one if you're looking for a formidable Pokémon to use.