Yes, you can find shiny Vulpix in Pokemon Go
CATCH NEW SHINY VULPIX IN POKÉMON GO!!! Shiny Ninetails Evolution!
Vulpix, the fox Pokémon from Kanto, is found in the wild in Pokémon Go. Yes, Vulpix can be shiny in Pokémon Go!
Vulpix and Ninetales both became shiny-eligible as part of a fall-themed event in October 2020. Note that this version of Vulpix should not be confused with its ice-type Alolan counterpart, which is also available shiny, but is separate.
According to old research from the now-defunct website The Silph Road (via the Wayback Machine), the shiny speed of Pokemon on a typical day is about one in 500. Vulpix is not a confirmed Pokemon that gets a "permaboost" (meaning it's a rare spawn and thus gain a boosted shine rate).