Antonyms for the phrase "runs up a flagpole" can include taking something down from a flagpole, removing or lowering a flag, or hiding or concealing an object. Instead of showcasing something publicly, antonyms may involve keeping it private or hidden away. In the context of politics or business, antonyms could involve avoiding unnecessary attention or scrutiny, instead of drawing attention to an issue or proposal. Other antonyms may include being discreet and keeping a low profile, rather than making a bold statement. In short, the antonyms for "runs up a flagpole" imply the opposite of drawing attention, emphasizing privacy and discretion over publicity.