The most common and most likely answer to this crossword clue is the 5 letter word WIELD
I've seen this crossword clue in The Guardian
W
I
E
L
D
More clues leading to the result WIELD
- Handle an old wit, the last to be promoted
- Energy required in violent exercise
- One involved in joint exercise
- Exercise in part of south-east England being reported
- Brandish one in joint
- Handle fuse I inserted
- I invested in bond to flourish
- Oddly rejected, oddly evil, we will head north and flourish
- Like a weed — just put energy in to make it flourish
- Flourish as one in union
Buddy explains!

The straight part
We know that "flourish" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flourish = wield.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 WIELD mean?
WIELD verb- To command, rule over; to possess or own.
- To control, to guide or manage.
- To handle with skill and ease, especially a weapon or tool.
- To exercise (authority or influence) effectively.