Not only did Christ preach the doctrine of reincarnation, but like the Buddhists, he also preached that it takes three days for the spirit to disengage itself completely from the physical body. As we are taught, Christ rose "on the third day."
I agree, there is a rich vein of reincarnational teaching in early Christian teachings, as there was in the Judaic and Egyptian religions, indeed it is littered with it as is the Christain-derived Gnostic teachings. Even some modern Catholic priests acknowledge it openly, such as Bishop Shelby Spong who has written extensively about it. Reincarnation, I believe, is the lost chord of Christianity.
I'm curious what your source is for this Buddhist belief. In the Tibetan Book of the Dead it is inferred that it takes forty nine days for the soul to pass through all the inner worlds before it can rest and move on. I'd be very interested to hear more of this three days idea.
You also wrote in another thread that Buddhists believe that it is hard to be reincarnated into a human body. I've heard this before too. I depends who you talk to or read though. Some Buddhists also say that we humans can be reincarnated into animals depending on how much merit we have acquired in earthly life and also by the quality of our actions. This idea jars severely with me. I am under the impression that "once a man always a man". Karma, if understood in its original sense as meaning "action" in an absolutely neutral way (like attracts like, cause and effect), must preclude us from reincarnating into the not only the body of an animal but also animals' emotional and mental bodies. I'm sure I read somewhere in Buddhist scripture that it is "elements" of the human constitution that are attracted to the other kingdoms - animal, mineral and plant - and help constitute bodies there WHILE our spiritual components i.e. consciousness journey through the inner worlds or "bardos".
As an aside, the idea that it is "harder" to reincarnate into a human body is interesting when we think about population growth. We don't know with any accuracy how much it has changed over the millennia but the world's population has increased over the past few decades although the actual figures are way off beam as far as "official" projections are concerned.