The most common and most likely answer to this crossword clue is the 6 letter word LOFTED
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More clues leading to the result LOFTED
Buddy explains!

The straight part
We know that "Had a fling" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case had a fling = lofted.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 LOFTED mean?
LOFTED verb- To propel high into the air.
- To fly or travel through the air, as though propelled
- To throw the ball erroneously through the air instead of releasing it on the lane's surface.
- To furnish with a loft space.
- (of a golf club) Having (a specified amount of) loft.
- Of a house: having more than one storey.
- Raised above the floor, so as to allow for storage etc. underneath.