Flight due, so desperately stealing kiss (6)
I believe the answer is:
exodus
'flight' is the definition.
(I know that exodus is a type of flight)
'due so desperately stealing kiss' is the wordplay.
'desperately' indicates an anagram.
'stealing' indicates putting letters inside.
'kiss' becomes 'x' (X can represent a kiss).
'due'+'so'='dueso'
'dueso' with letters rearranged gives 'eodus'.
'eodus' going around 'x' is 'EXODUS'.
(Other definitions for exodus that I've seen before include "Mass leaving" , "Second book of the Old Testament" , "A mass departure, as in O.T. book" , "Mass departure of people as of Jews from Egypt" , "Mass migration (of a people)" .)