Safe from the flood — keeping daughter oblivious (2,3,4)
I believe the answer is:
in the dark
'oblivious' is the definition.
(in the dark can mean unaware of something)
'safe from the flood keeping daughter' is the wordplay.
'safe from the flood' becomes 'in the ark' (on board Noah's ark).
'keeping' is an insertion indicator.
'daughter' becomes 'd' (genealogical abbreviation).
'intheark' enclosing 'd' is 'IN THE DARK'.
(Other definitions for in the dark that I've seen before include "Lacking information" , "without being informed" , "Ignorant, unaware" , "Without information" , "without being told" .)