As a collection of fascinating ideas about the development of modern human consciousness... fantastically well. Modern ideas from all over the place: science fiction, human history, philosophy, spiritualism and even computer science have broadly moved closer to Jaynes' way of thinking.
One exception is his definition of consciousness. We still don't really have a single definition, and every "theory" tends to define it different. But overall, Jaynes' doesn't mesh too well with most current definitions. We're much more likely to consider animals conscious today, for example. You might substitute "introspective consciousness."
In particular, modern notions that "consciousness is a simulation/projection" work well with Bicameral Mind.
For the rabbit-holers:
https://en.wikipedia.org/wiki/Robert_Monroe
Related: https://www.cia.gov/readingroom/docs/CIA-RDP96-00788R0017002...
Also related, recording: https://archive.org/details/monroe-institute-explorer-series...
If you're worried that science had made this book obsolete in any way - don't. It's philosophy, not applied science.
Or, in other words, becomes science.
Philosophy is full of demonstrably false ideas where science has caught up and been able to test and find the truth of something, especially in the areas of philosophy of mind.
Which is fine, honestly. Somebody else here compared him with Freud. Exploratory thinking about the natural world can still be worth reading even if much of it later turns out to be incorrect.
I heard about the book when I watched Westworld, but apparently all the theory is based on some historical stories, of which no ones how accurate they really are.
But it is also not true that it is only based on that. It also builds on then-contemporary research about schizophrenia, hearing voices, and other things.