The most common and most likely answer to this crossword clue is the 6 letter word JETTED
J
E
T
T
E
D
Buddy explains!

The straight part
We know that "flew" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flew = jetted.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does JETTED mean?
JETTED verb- To spray out of a container.
- To spray with liquid from a container.
- To travel on a jet aircraft or otherwise by jet propulsion
- To move (running, walking etc.) rapidly around
- To shoot forward or out; to project; to jut out.
- To strut; to walk with a lofty or haughty gait; to be insolent; to obtrude.
- To jerk; to jolt; to be shaken.
- To adjust the fuel to air ratio of a carburetor; to install or adjust a carburetor jet
- To leave.