On reflection, look into Native American cooking style (6)
I believe the answer is:
creole
'cooking style' is the definition.
(I've seen this in another clue)
'on reflection look into native american' is the wordplay.
'on reflection' says the letters should be written backwards.
'look' becomes 'lo' ('lo' is an archaic exclamation meaning 'look!').
'into' indicates putting letters inside.
'native american' becomes 'cree' (an indigenous people of North America).
'lo' backwards is 'ol'.
'ol' put within 'cree' is 'CREOLE'.
(Other definitions for creole that I've seen before include "Descendant of French settlers as in New Orleans" , "Person of European descent born in W Indies" , "White descendant of French ancestors as in New Orleans" , "One of mixed descent" , "Descendant of French settlers in Louisiana" .)