Reincarnation is the philosophical or religious concept that the non-physical essence of a living being starts a new life in a different physical form or body after biological death. It is also called rebirth or transmigration, and is a part of the Saṃsāra doctrine of cyclic existence. It is a central tenet of Indian religions, namely Jainism, Buddhism, Sikhism and Hinduism, although there are Hindu groups that do not believe in reincarnation but believe in an afterlife.
Allah (SWT) created our spirits before creating our bodies as we read in Hadeeths. Our spirit will leave our body when we leave this world in death. No question of incarnation at all. Every spirit is for the same person and will ever go into another persons body. Allah (SWT) does not lack ability to create spirits for every creature and does not need to incarnate a soul or spirit into another person or creature. It is also against justice to believe in incarnation because it amounts on imposing behavior of a person on another person.
Incarnation claim is a myth .