Should this not be "Nein, keine Blumen"....?
Just curious, but wouldn't Keine be used if there was an article (a or an) before Blumen?
for example: an apple = Ein Apfel, not an apple = Kein Apfel.
because there was no article before Blumen, Keine could have no place.
Afaik, 'keine' = 'nicht eine', so that will be 'no, not a flower', small difference.
This must be "Nein, keine Blumen" because you are negating a noun not a verb.