The most common and most likely answer to this crossword clue is the 6 letter word LAPPET
I've seen this crossword clue in The Daily Telegraph
L
A
P
P
E
T
More clues leading to the result LAPPET
Buddy explains!

The straight part
We know that "a wee flap" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a wee flap = lappet.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 LAPPET mean?
LAPPET noun- A small decorative fold or flap, especially of lace or muslin, in a garment or headdress.
- A wattle or flap-like structure on the face.
- A head-dress made with lappets for lace pendants.
- Lobe (division of an organ).
- To decorate with, or as if with, lappets.