Bird that could make dog flinch (9)
I believe the answer is:
goldfinch
'bird' is the definition.
(goldfinch is a kind of bird)
'could make dog flinch' is the wordplay.
'could make' indicates an anagram.
'dog'+'flinch'='dogflinch'
'dogflinch' is an anagram of 'GOLDFINCH'.
'that' is the link.
(Other definitions for goldfinch that I've seen before include "Singer" , "flier?" , "Small bird with yellow and black wings" , "Bird with yellow body plumage" , "Colourful garden bird" .)