The term "fly about" means to move or soar in an unhurried, aimless manner. There are several synonyms that can be used in its place. One of them is "hover," which means to remain in one place while staying in motion. Another synonym is "flutter," which describes a rapid but light movement in the air. "Drift" is also a good option, indicating a motion that is slow and gradual. Other synonyms include "flit," "flitter," "swoop," and "circulate." Using these synonyms adds color and variety to writing, ensuring that readers remain engaged and interested.