Flushed with a bit of square dancing (3)
I believe the answer is:
red
'flushed' is the definition.
('red' can be a synonym of 'flushed')
'a bit of square dancing' is the wordplay.
'a bit of' indicates a hidden word (I've seen 'a bit' mean this (the answer is formed by a bit of the clue)).
'RED' is hidden in the letters of 'square dancing'.
'with' is the link.
(Other definitions for red that I've seen before include "Ruby" , "Crimson" , "14 -- breed of 4" , "See it and become angry" , "eg Cardinal" .)