I am writing a memoir and want to use some quotes from the King James Version Bible. Will this be considered Public Domain because of the age.
Yes, it will. Quote away, without fear of being attacked for not footnoting what you are quoting.
In the Wikipedia article on the KJV, you'll find the following: "The Authorized Version [i.e., the KJV] is in the public domain in most of the world."
In your memoirs, just make sure your quotation corresponds to the correct chapter and verse. A personal pet peeve of mine is the frequency with which I go to the reference provided in a writing and fail to find the verse that is quoted and cited.
On the plus side, however, that kind of erratum makes me appreciate all the more the miraculous job performed by generations of faithful and meticulous scribes and transcribers who all did their part in providing us with the Bible we have today. PTL!