The coat you might be thinking of is the black coat with the red hood that he wears in Kingdom Hearts: Chain of Memories. This coat is not an Organization coat.
While it shares some stylistic similarities with the coats worn by members of Organization XIII, King Mickey's coat is unique. It is a symbol of his determination to fight against the darkness, and it represents his role as a protector of light.
It's important to remember that the Organization XIII coats are specifically designed to represent their membership in the organization, with their distinctive number markings and color scheme.
King Mickey's coat, on the other hand, has its own unique design and is not associated with the Organization in any way.