Yes, the days of Noah are referred to in the New Testament, but even Isaiah waxes eloquent about the promises God made.
And the rainbow displays its promise again, Aug 3, 2017 over the White House. It means different things for different administrations.
Then in Revelation the rainbow is mentioned again,
Ka’b al –Ahbar (ca 652 A.D) wrote that Ham lay with his wife and gave birth to a black boy and girl. He claimed they were not his. They are, his wife responded “for the curse of your father is upon us.” The story goes on, and all blacks come out from four black children of Ham. Wahb ibn Munabbih (ca 730 A.D.) wrote that Ham was a fine white man, but because of his Father’s curse God Almighty changed his skin color to black. He then became the father of all the black people. In the story collection “One Thousand and One Nights, A.K.A Arabian Nights” it is also found: Noah blessed Shem and Cursed Ham. (Source: The curse of Ham. By David M. Goldenberg)