This page has all the references to reincarnation(s) and transmigration:
(86:4.6) The orange race was especially given to belief in transmigration and reincarnation. This idea of reincarnation originated in the observance of hereditary and trait resemblance of offspring to ancestors. The custom of naming children after grandparents and other ancestors was due to belief in reincarnation. Some later-day races believed that man died from three to seven times. This belief (residual from the teachings of Adam about the mansion worlds), and many other remnants of revealed religion, can be found among the otherwise absurd doctrines of twentieth-century barbarians.
(88:1.4) If an animal ate human flesh, it became a fetish. In this way the dog came to be the sacred animal of the Parsees. If the fetish is an animal and the ghost is permanently resident therein, then fetishism may impinge on reincarnation. In many ways the savages envied the animals; they did not feel superior to them and were often named after their favorite beasts.
(94:2.3) The undue concentration on self led certainly to a fear of the nonevolutionary perpetuation of self in an endless round of successive incarnations as man, beast, or weeds. And of all the contaminating beliefs which could have become fastened upon what may have been an emerging monotheism, none was so stultifying as this belief in transmigration — the doctrine of the reincarnation of souls — which came from the Dravidian Deccan. This belief in the weary and monotonous round of repeated transmigrations robbed struggling mortals of their long-cherished hope of finding that deliverance and spiritual advancement in death which had been a part of the earlier Vedic faith.
(94:2.6) These were the times of the compilation of the later scriptures of the Hindu faith, the Brahmanas and the Upanishads. Having rejected the teachings of personal religion through the personal faith experience with the one God, and having become contaminated with the flood of debasing and debilitating cults and creeds from the Deccan, with their anthropomorphisms and reincarnations, the Brahmanic priesthood experienced a violent reaction against these vitiating beliefs; there was a definite effort to seek and to find true reality. The Brahmans set out to deanthropomorphize the Indian concept of deity, but in so doing they stumbled into the grievous error of depersonalizing the concept of God, and they emerged, not with a lofty and spiritual ideal of the Paradise Father, but with a distant and metaphysical idea of an all-encompassing Absolute.
(94:7.3) Amid the confusion and extreme cult practices of India, the saner and more moderate teachings of Gautama came as a refreshing relief. He denounced gods, priests, and their sacrifices, but he too failed to perceive the personality of the One Universal. Not believing in the existence of individual human souls, Gautama, of course, made a valiant fight against the time-honored belief in transmigration of the soul. He made a noble effort to deliver men from fear, to make them feel at ease and at home in the great universe, but he failed to show them the pathway to that real and supernal home of ascending mortals—Paradise—and to the expanding service of eternal existence.
(130:2.8) That afternoon Jesus and Ganid had both enjoyed playing with a very intelligent shepherd dog, and Ganid wanted to know whether the dog had a soul, whether it had a will, and in response to his questions Jesus said: “The dog has a mind which can know material man, his master, but cannot know God, who is spirit; therefore the dog does not possess a spiritual nature and cannot enjoy a spiritual experience. The dog may have a will derived from nature and augmented by training, but such a power of mind is not a spiritual force, neither is it comparable to the human will, inasmuch as it is not reflective—it is not the result of discriminating higher and moral meanings or choosing spiritual and eternal values. It is the possession of such powers of spiritual discrimination and truth choosing that makes mortal man a moral being, a creature endowed with the attributes of spiritual responsibility and the potential of eternal survival.” Jesus went on to explain that it is the absence of such mental powers in the animal which makes it forever impossible for the animal world to develop language in time or to experience anything equivalent to personality survival in eternity. As a result of this day’s instruction Ganid never again entertained belief in the transmigration of the souls of men into the bodies of animals.
(164:3.4) There was, throughout all these regions, a lingering belief in reincarnation. The older Jewish teachers, together with Plato, Philo, and many of the Essenes, tolerated the theory that men may reap in one incarnation what they have sown in a previous existence; thus in one life they were believed to be expiating the sins committed in preceding lives. The Master found it difficult to make men believe that their souls had not had previous existences.
(37:10.3) The Spornagia. The architectural headquarters worlds of the local universe are real worlds—physical creations. There is much work connected with their physical upkeep, and herein we have the assistance of a group of physical creatures called spornagia. They are devoted to the care and culture of the material phases of these headquarters worlds, from Jerusem to Salvington. Spornagia are neither spirits nor persons; they are an animal order of existence, but if you could see them, you would agree that they seem to be perfect animals.
(46:7.4) Although spornagia neither possess nor evolve survival souls, though they do not have personality, nevertheless, they do evolve an individuality which can experience reincarnation. When, with the passing of time, the physical bodies of these unique creatures deteriorate from usage and age, their creators, in collaboration with the Life Carriers, fabricate new bodies in which the old spornagia re-establish their residences.
(46:7.5) Spornagia are the only creatures in all the universe of Nebadon who experience this or any other sort of reincarnation. They are only reactive to the first five of the adjutant mind-spirits; they are not responsive to the spirits of worship and wisdom. But the five-adjutant mind equivalates to a totality or sixth reality level, and it is this factor which persists as an experiential identity.