The most common and most likely answer to this crossword clue is the 7 plus 8 letter word CHINESE LANTERNS
I've seen this crossword clue in The Guardian
C
H
I
N
E
S
E
L
A
N
T
E
R
N
S
Buddy explains!
The straight part
We know that "they go up in flames" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they go up in flames = chinese lanterns.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.