Wikipedia and most dictionary definitions talk about uniqueness. Each snowflake is unique. That’s what most people mean by it.
Snowflake is a derogatory slang term for a person, implying that they have an inflated sense of uniqueness, an unwarranted sense of entitlement, or are overly emotional, easily offended, and unable to deal with opposing opinions.
You are not special. You are not beautiful or unique snowflake. Quote from the novel “Fight Club”