There are several synonyms for the phrase "runs flagpole." One common phrase that is often used interchangeably is "hoists flagpole." This refers to the action of pulling a flag up to the top of the flagpole. Another synonym for "runs flagpole" is "raises flagpole," as this phrase refers to the same action of elevating a flag to the top of the pole. Additionally, "flies flagpole" can be used as a synonym for "runs flagpole," as both phrases convey the idea of displaying a flag on a pole in a public setting. Overall, these synonyms can be used to convey the same idea of displaying a flag on a flagpole.