The most common and most likely answer to this crossword clue is the 8 letter word CALMNESS
I've seen this crossword clue in The Guardian
C
A
L
M
N
E
S
S
More clues leading to the result CALMNESS
Buddy explains!

The straight part
We know that "Unflappability" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unflappability = calmness.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 CALMNESS mean?
CALMNESS noun- The state of being calm; tranquillity; silence.
- The product of being calm.