The most common and most likely answer to this crossword clue is the 7 letter word SARCOMA
I've seen this crossword clue in Financial Times
S
A
R
C
O
M
A
More clues leading to the result SARCOMA
Buddy explains!
The straight part
We know that "fleshy growth" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fleshy growth = sarcoma.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 SARCOMA mean?
SARCOMA noun- A type of malignant tumor of the bone, cartilage, fat, muscle, blood vessels, or other connective or supportive tissue.