The phrase "flies about" is often used to describe something that moves quickly or circulates widely. Synonyms for this phrase include "circulates," "whips around," "flies around," "buzzes around," "zips around," and "swarms around." These words all convey a sense of rapid movement or activity, whether it be people, rumors, or objects. Other synonyms for "flies about" may depend on the context in which it is used. For example, if referring to a rumor, synonyms could include "spreads," "circulates," or "gossips." No matter what the context, there are plenty of words to replace "flies about" and add more variety to your writing.