The most common and most likely answer to this crossword clue is the 7 plus 3 plus 5 letter word SCRATCH AND SNIFF
I've seen this crossword clue in The Guardian
S
C
R
A
T
C
H
A
N
D
S
N
I
F
F
Buddy explains!
The straight part
We know that "What dog with fleas and a cold might do/with essence as yet undiscovered" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what dog with fleas and a cold might do/with essence as yet undiscovered = scratch and sniff.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.