The most common and most likely answer to this crossword clue is the 9 letter word RAZORBILL
I've seen this crossword clue in The Guardian
R
A
Z
O
R
B
I
L
L
More clues leading to the result RAZORBILL
Buddy explains!

The straight part
We know that "a flyer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a flyer = razorbill.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 RAZORBILL mean?
RAZORBILL noun- A large black and white auk, Alca torda, native to the north Atlantic.