There are several synonyms for the phrase "flies back" that can be used in different contexts. For example, "returns by air" implies the individual is returning home or to a specific destination via airplane. "Reverts to" could imply a change in behavior or progression back to an earlier state. "Retreats" could mean physically or mentally retreating from a situation. "Regains momentum" could be used in regards to a project or effort that had stalled but is now picking up speed again. "Resurges" implies a similar situation where something that had slowed down is now coming back stronger. Overall, there are many ways to express the idea of "flies back" depending on the context and desired connotation.