The most common and most likely answer to this crossword clue is the 8 letter word FLAUNTED
I've seen this crossword clue in The Daily Telegraph
F
L
A
U
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D
Buddy explains!

The straight part
We know that "Waved proudly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case waved proudly = flaunted.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 FLAUNTED mean?
FLAUNTED verb- To wave or flutter smartly in the wind.
- To parade, display with ostentation.
- To show off, as with flashy clothing.
- To flout.