Jaynes bought into the evolutionay paradigm. His studies indicated that people living between he times of Exodus and of Alexander were using a part of the brain which is no longer used in such a way as to produce what he called "auditory hallucinations" and that entire societies were being controlled by such hallucinations at the time of the Trojan war. At every point at which you or I would have to make a decision, those people were being told what to do by inner voices which they called gods and goddesses. Another way to interpret the same findings is to entertain the notion that human language prior to the flood and the tower of Babel had been telepathic and that what was going on at the time of the Trojan war was a broken remnant of that former capability.
All of that had nothing to do with the flood itself of course, the flood was a real event, but a natural event. It takes a sorry opinion of God to imagine that he would wipe the entire solar system for sin only to have sin back in business a few decades later as if nothing had happened.
It takes a sorry opinion of God to imagine that he would wipe the entire solar system for sin only to have sin back in business a few decades later as if nothing had happened. There are many who believe God used the Flood to remove the nephilim from the earth (as the Book of Enoch and others so plainly explain).
I have never noticed that Jaynes bought into the theory of evolution. The origin of consciousness is only about the transformation you mention of moving from dependence on auditory perceptions to acting independently from such perceptions because they grew increasingly faint.