The most common and most likely answer to this crossword clue is the 7 letter word COMBUST
I've seen this crossword clue in Financial Times
C
O
M
B
U
S
T
More clues leading to the result COMBUST
Buddy explains!
The straight part
We know that "to go up in flames" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to go up in flames = combust.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 COMBUST mean?
COMBUST noun- That which undergoes burning.
- To burn; to catch fire.
- To erupt with enthusiasm or boisterousness.
- Burnt.
- In close conjunction with the sun (so that its astrological influence is "burnt up"), sometimes specified to be within 8 degrees 30'.