The most common and most likely answer to this crossword clue is the 5 plus 5 letter word TAWNY EAGLE
I've seen this crossword clue in Financial Times
T
A
W
N
Y
E
A
G
L
E
More clues leading to the result TAWNY EAGLE
Buddy explains!
The straight part
We know that "flyer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flyer = tawny eagle.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.