Clear the mess made by Flash, the dog? (3,2)
I believe the answer is:
mop up
'clear the mess' is the definition.
'by flash the dog?' is the wordplay.
'by' means one lot of letters go next to another.
'flash' becomes 'mo' (I've seen this in other clues).
'the dog?' becomes 'pup' (I have seen 'Young dog ' mean 'pup' so perhaps 'dog' could also mean 'pup').
'mo' next to 'pup' is 'MOP-UP'.
'made' is the link.
(Other definitions for mop up that I've seen before include "Finish off a task, clean away remnants" , "Swab" , "Finish a task, clear away remnants" , "Kill (enemy stragglers)" , "Deal with spillage or defeated enemy" .)