The purpose of creating a Dark Brown Missing Cat Flyer is to spread awareness and seek help in locating a missing pet. The flyer includes details about the cat's appearance, name, and contact information of the owner, making it easier for people to spot the cat and contact the owner if they see it. The creation and distribution of flyers in the neighborhood, online and in local businesses help increase the chances of a successful reunion with the missing cat, providing peace of mind for the owner.