I have a fiction where I need to reference why the great flood in Noah's day and when man turned back to evil after the flood. Is it legal to reference a Bible story?
This is more of a legal question and a literary question in general. As pointed out, the King James Version and others are in public domain and therefore should be free to reference (not rewrite verbatim).
I think the question for the legality and literary porion would ask is "how" you are planning on referencing the story. Is there an excerpt or chapter that or segment of the fiction that will have the story word for word? Or will a character be paraphrasing as they are talking about story within your fiction piece? Or possibly somewhere in between? Or something very different? Is the reference in the fiction actually a reference to another fiction referencing that story? Or possibly the reference is to another historical document that references the story? Or again, some where in between?
These are questions made for you to think about it which will change the legal frame of reference. This is not meant to be answered here, but more of a rhetorical question to think about and then ask someone with some legal background.
Very general, there may be some general disagreements and debates over the story of Noah in the Christian communities (and outside as well), but as long as the reference isn't controversial, offensive, rude, a mockery, misleading, or taken completely out of context there shouldn't be an issue with referencing the story.