The most common and most likely answer to this crossword clue is the 6 letter word HACKLE
I've seen this crossword clue in Financial Times
H
A
C
K
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More clues leading to the result HACKLE
Buddy explains!

The straight part
We know that "fly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fly = hackle.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 HACKLE mean?
HACKLE noun- An instrument with steel pins used to comb out flax or hemp.
- (usually now in the plural) One of the long, narrow feathers on the neck of birds, most noticeable on the rooster.
- A feather used to make a fishing lure or a fishing lure incorporating a feather.
- (usually now in the plural) By extension (because the hackles of a rooster are lifted when it is angry), the hair on the nape of the neck in dogs and other animals; also used figuratively for humans.
- A plate with rows of pointed needles used to blend or straighten hair.
- A feather plume on some soldier's uniforms, especially the hat or helmet.
- Any flimsy substance unspun, such as raw silk.
- To dress (flax or hemp) with a hackle; to prepare fibres of flax or hemp for spinning.
- To separate, as the coarse part of flax or hemp from the fine, by drawing it through the teeth of a hackle or hatchel.
- To tear asunder; to break into pieces.