There is evidence that reincarnation does exist all around us, even in nature.
A bulb flower regenerates itself every season reincarnating its self each year for us to behold its beauty. When you have cases of dejuvu feelling like you have done or seen something before. It is because you have in a previous past life. When meeting someone for the very 1st time and you feel like you have known them forever. Its because your spirit recognizes theirs from a previous lifetime.
The reason why reincarnation does exist is because there is way too many lessons for our spirits to learn both sides of every single one of them in just one lifetime. So we are continually reincarnated until all leasons are learned. We as souls have our choices as to when and where we will be reincarnated into to best learn our next sets of lessons. We decide before we are even born whom our parents will or will not be.
One of the good things about reincarnation is the fact that once we have learned something we never have to go through it again. As an example lets say in this lifetime you passed away due to a horendous disease such as cancer or aids. Well in your future lifetimes when you decide to be reincarnated you will not have to worry about getting those illnesses ever again.
Another way to prove reincarnation does exist is when you know things that there is no way of you knowing in this lifetime because you have never been taught it or seen or heard of it before. Like being in a totally strange place but knowing exactly what lies ahead around the corner.
All the above is evidence that reincarnation does exist.