I don't understand reincarnation at all. A person is who they are based on their experiences, which shape them, and the environment and time they live in. That means you are you because of the country you were born/ live in, the language you speak, the shared culture you are a part of, the sex you are, the people you know and the path through life you take.
So... you live your life. Die. And are born again in a different country, on the other side of the world. You are the opposite sex, it is several decades later (maybe centuries) which means belief, knowledge and societal norms have changed radically, you are a different faith/ no faith, you get a different education, you know and love completely different people, you hold different values and you have no memory of your previous life How the fuck are you the same person? How is this new person you?
Even pretending the existence of a soul is real and actual thing and that a soul can move around ... if it passes on no knowledge and memory of its last time around what is the point of it? What is its purpose? What is its essence? How is it you?
Reincarnation - the passing on of a soul to another body - kind of suggests that the soul is the important part of a human - that you are the soul and your body is just the vehicle the soul moves through. But if the soul has no memory - and differing experiences shapes a whole different person - what is the soul? Why is important? The person you were is dead. The new body of the soul has no memories of the old, has no links to their old family ... but the soul is the important bit that makes you you no matter how many bodies it hops into?
What exactly has been reincarnated - if you don't remember the last time around? It's not your body. It's not your personality. It's not your knowledge and experience. What has come back? What of you has actually come back?
If the soul doesn't bring knowledge and experience and personality traits, then it is at best like the engine of your body: the divine spark that moves you around. And the divine spark moves from body to body - but it clearly isn't sentient, because it doesn't take anything with it - we don't even know it's really there when it's inside of us. So it's just energy moving around but ... that then suggests that the energy is you, rather than your experiences and memories, and not just the thing moving you around. I'm afraid I think people are more complex and interesting than the amorphous blob of energy that drives them - it isn't that unknown, unseen, unproven essence that we love in our loved ones, or shapes ourselves. I think the idea that this 'soul' or 'energy' is what is actually meaningful about you does people a huge disservice. It's like taking the batteries out of your remote control, sticking them in a torch and then claiming that the remote was reincarnated as a torch. That's not what's happened. The power source has moved on - and the remote is now essentially dead.
So even if the same 'life force'/ 'soul'/ whatever that powered Joan of Arc is now inside of you - you are not Joan of Arc. You don't have her memories, you didn't live her life, you don't share her experiences - you probably don't share her values or beliefs. You are you. Joan of Arc is Joan of Arc. You just shared a battery. Just think of your own sense of self, your own lived experiences and how vivid all that is. You know full well that you're not somebody else, as well, or that one day you will be somebody else in the future. You have no 'Joan of Arc' sense of self - because you're not her.
Joan of Arc is dead and gone, and one day you will be - even if the battery moves on. And in this case, there is nothing left of her or you - because the 'soul' is now a brand new person who remembers neither - that seems a heck of a lot less comforting, and a heck of a lot more final than the idea of an afterlife. You are gone and the person now using your battery doesn't care or know - so the battery was never you.
I'm not saying this impossible - just that it really isn't worth giving a name to. It's swapping batteries. It's meaningless. The idea that you come back as a King or a Dung Beetle is a nonsense - your battery is recycled. You are dead.
Whilst I don't subscribe to the existence of souls or life after death, the pointlessness of a soul does not hold true in such belief systems - because the soul is you, in that when it moves on it remembers your life, loves who you loved - but is now in immortal form. Reincarnation is just unplugging you and plugging someone else into the same socket. And you are even more dead, because it turns out that soul was never 'yours'. It was a loaner.
To a certain extent the movement of energy being 'reincarnation' is fair enough. Energy can't be destroyed so it transfers into some other form - so to an extent you are 'reincarnated' in a less orderly form as the molecules that were you change into something else (but not one other thing - you disperse). But that is not the same as having once been Florence Nightingale and - again - is not really worth giving a name to, certainly not worth building some kind of spiritual belief around.
As for the weird things little children 'remember' - adults always underestimate how much tiny children hear and absorb. Children hear everything that is spoken over their heads, when grownups think they're not listening. They hear everything on the television. They don't understand everything, but they can repeat it back verbatim. Long after the adults forget they ever said the thing the child is repeating back to them as 'knowledge they couldn't possibly have.'
It's why it stops at about age 5 - not only are their brains less super absorbent as they get older, but as they get older you become more aware of what you're saying in front of them - what is on the television whilst they're in the room. They just don't have the same access to the info to repeat back at a later time and freak you out. And of course - the older they get - the better at understanding the difference between reality and make believe they get, they keep the stuff they make up in their head because they know it's not real. Tiny children don't have that filter - and get dreams, things they saw on the t.v and conversations they've overheard mixed up with reality.