If it is of interest to anyone -
Buddhists do not believe in reincarnation as Hindus do, they believe in rebirth - a bit tricky to describe i'll try to be brief.
The Three Lakshanas underpin Buddhism, they are what make up reality - Dukka (suffering) Anicca (Impermenance) and Anatta (for briefness here, I will describe this as a lack of a soul/self). This thread I think is talking about Anicca and Anatta.
Buddhists believe everything to be impermanent (apart for Nibbana but that's a whole other discussion) and this links closely to the idea that humans do not have a consistent, eternal 'self'. Hence reincarnation is not applicable to Buddhism as their is no 'self' to be transplanted into a new life. The self - both our physical bodies and our conceptual idea of 'self' - is impermanent and our attatchment to both causes Dukka. Everything requires conditioned and contingent existence in Buddhism - Pratītyasamutpāda - and our bodies are as dependant on other things as much as everything else in this world. We do not own our bodies because the conditions that gave rise to it do, and those conditions will change hence our bodies will change. Any attatchment to something that will change and eventually die will lead to Dukka.
Buddhists (in most traditions I think, but you do get secular Buddhists who are a bit less literal with it) believe we are made up of 5 Skhandas which include Rupa (form) and mental perception. Rebirth entails these Skhands transferred to different beings. There is no singular 'self'. King Milinda's Questions of The Chariot describes this well through similie. Taken fromna religious studies website -
But what is a chariot? Nagasena asked. Is it the wheels, or the axles, or the reigns, or the frame, or the seat, or the draught pole? Is it a combination of those elements? Or is it found outside those elements?
The King answered no to each question. Then there is no chariot! Nagasena said.
Now the King acknowledged the designation "chariot" depended on these constituent parts, but that "chariot" itself is a concept, or a mere name.
Just so, Nagasena said, "Nagasena" is a designation for something conceptual. It is a mere name. When the constituent parts are present we call it a chariot; When the Five Skandhas are present, we call it a being.
Nagasena added, " This was said by our sister Vajira when she was face to face with the Lord Buddha." Vajira was a nun and a disciple of the historical Buddha. She used the same chariot simile in an earlier text, the Vajira Sutta (Pali Sutta-pitaka, Samyutta Nikaya 5:10). However, in the Vajira Sutta the nun was speaking to the demon, Mara.
Another way to understand the chariot simile is to imagine the chariot being taken apart. At what point in the dis-assembly does the chariot cease to be a chariot? We can update the simile to make it an automobile. As we disassemble the car, at what point is it not a car? When we take off the wheels? When we remove the seats? When we pry off the cylinder head?