The flood story has one of the most universal covenants of the Old Testament.

It really should be known as "God and the Flood" rather than "Noah and the Flood" - poor old Noah doesn't even have a speaking role in the story until well after the rainbow. The story is in Genesis 6-9, and there are actually two covenants explicitly mentioned. In fact, there's a lot more to this story than most children's-book retellings would suggest!