The most common and most likely answer to this crossword clue is the 13 letter word YANKEE-DOODLE
I've seen this crossword clue in The Guardian
Y
A
N
K
E
E
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D
O
O
D
L
E
More clues leading to the result YANKEE-DOODLE
Buddy explains!
The straight part
We know that "American dandy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case american dandy = yankee-doodle.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.