In his recent book A. Robert Smith makes a case for reincarnation. He talks of his experiences as the founding Editor of Venture Inward Magazine published by the Edgar Cayce foundation. He refers to all the studies of children born with detail memories of past lives. https://www.amazon.com/Roberts-Rules-Order-Good-Life-ebook/dp/B01FCQJW1Y
In Jesusgate A History of Concealment Unraveled, the author speaks of the multitude of now thought to be exotic beliefs that many diverse Christian groups and sects had among them many forms of reincarnation before the Council of Nicea in 325 AD banned all but the agreed on bible. https://www.amazon.com/Jesusgate-Concealment-Unraveled-Ernie-Bringas-ebook/dp/B00BD63AM0/ref=sr_1_1?s=digital-text&ie=UTF8&qid=1471002416&sr=1-1&keywords=jesusgate
The first time I went to Peru in 1973 I had many visions of Inca Gods and Goddesses. Who informed me that I had made a deal with them in a past life in the Inca Empire. https://www.amazon.com/Secrets-Ancient-Incas-Approach-Practice-ebook/dp/B001BQ9058/ref=sr_1_1?s=apparel&ie=UTF8&qid=1471002511&sr=8-1&keywords=langevin+The+secrets+of+the+ancient+inca
I have returned to Latin America often since then and been lucky, blessed and persistent enough to find many authentic shamans to study with and do ritual and ceremony with. Their views on reincarnation run a large gamut. Some see it very simply. You live you die you are reborn over and over and over. Most have much more in depth views on life after death. Most feel we have choices. We have many levels to our being/ soul and each level has choices. We are made up of pieces of many beings who lived before and each piece has choices. We can choose to be ghosts or cease to exist or exist in our belief system or in our fantasy world. We can split our being/soul after death part of us can stay on earth to finish work as a spirit, part can go evolving in the astral planes, part can sit in a place those who think of us can visit in trance or dreams, part can reincarnate.
I think it funny Christianity does not teach about simple reincarnation but even funnier that few spiritual teachers take on the teaching of the complex Latin American Shamanic views of life after death.