The most common and most likely answer to this crossword clue is the 8 letter word PERISHER
I've seen this crossword clue in Financial Times
P
E
R
I
S
H
E
R
Buddy explains!
The straight part
We know that "Flibbertigibbet/who’s done for" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flibbertigibbet/who’s done for = perisher.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 PERISHER mean?
PERISHER noun- An annoying child, a brat.
- One who perishes.
- An extreme.