The most common and most likely answer to this crossword clue is the 6 letter word WAVING
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Buddy explains!

The straight part
We know that "flapping" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flapping = waving.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 WAVING mean?
WAVING verb- To relinquish (a right etc.); to give up claim to; to forego.
- To put aside, avoid.
- To outlaw (someone).
- To abandon, give up (someone or something).
- To move from side to side; to sway.
- To stray, wander.
- To move back and forth repeatedly and somewhat loosely.
- To move one’s hand back and forth (generally above the shoulders) in greeting or departure.
- (metonymic) To call attention to, or give a direction or command to, by a waving motion, as of the hand; to signify by waving; to beckon; to signal; to indicate.
- To have an undulating or wavy form.
- To raise into inequalities of surface; to give an undulating form or surface to.
- To produce waves to the hair.
- To swing and miss at a pitch.
- To cause to move back and forth repeatedly.
- (metonymic) To signal (someone or something) with a waving movement.
- To fluctuate; to waver; to be in an unsettled state.
- To move like a wave, or by floating; to waft.
- The motion of something that waves.
- Repeated moving of arms or hands to signal.