The most common and most likely answer to this crossword clue is the 6 letter word OOZING
I've seen this crossword clue in Financial Times
O
O
Z
I
N
G
Buddy explains!

The straight part
We know that "flowing slowly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flowing slowly = oozing.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 OOZING mean?
OOZING verb- To be secreted or slowly leak.
- To give off a strong sense of (something); to exude.
- Something that oozes; a seepage.