A sun dog is an atmospheric optical phenomenon that consists of a bright spot separated by 22° from the Sun to one or both sides of the Sun. It is caused by the refraction of sunlight by ice crystals in the atmosphere.
Flat-Earthers claim that a sun dog is caused by the reflection of sunlight by the mythical dome enclosing the flat Earth, that there are multiple suns, or other equally implausible reasons. They are wrong. A sun dog is simply an optical phenomenon that occurs in cold locations where ice crystals can accumulate in the atmosphere.