There are many synonyms for the phrase "red dog" that can be used to describe a canine with a reddish coat. Some of these synonyms include red retriever, red setter, red hound, Irish setter, and golden retriever. All of these synonyms describe various breeds or mixes of dogs that can have a red or reddish coat. Additionally, some other phrases that could be used to describe a red dog might include "chestnut-colored canine" or "ruby-furred pooch." Whatever the specific phrase used, it's clear that there are many synonyms and descriptions that can accurately depict a dog with a red coat.