The most common and most likely answer to this crossword clue is the 10 letter word EXACERBATE
I've seen this crossword clue in The Daily Telegraph
E
X
A
C
E
R
B
A
T
E
More clues leading to the result EXACERBATE
- Provoke retired pilot to assess penning book
- Provoke former top judge about British
- Aggravate former partner over account and berate in error
- To make matters worse former champion facing cut missing middle of green
- Inflame former wife with perfect figure hugging bachelor
- To make matters worse, former pro running back had a meal
- Provoke cut back on dubious race bet
Buddy explains!

The straight part
We know that "Inflame" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case inflame = exacerbate.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 EXACERBATE mean?
EXACERBATE verb- To make worse (a problem, bad situation, negative feeling, etc.); aggravate; exasperate.