The above and following figure and the following text is from Lucy Lamy, Egyptian Mysteries; p.26 (Thames & Hudson, Art and Imagination Series). I have added my comments.
"The mortal body kha is animated during its existence by the ba, written with a migratory bird, the Jabiru or stork, accompanied by a pot with a flame burning in it," (left)
In the Shakta Tantric iconography the Jivatman or Soul is said to dwell in the Anahata (Heart) Chakra in the form of a flame.
"or else represented in the form of a human-headed bird fluttering about the tomb near the dead person."
"The ba also plays a role in cosmogenesis....The soul, ba, of Shu was the fire produced by Atum at the moment of the initial creative emission of semen. Likewise the Creator "made metamorphoses starting from this, his ba", the ba thus playing the role of the determining individualizing force, the first active principle, parallel to the first coagulation, the disruption of the inertia in the cosmic ocean."
There are parallels here with the Neoplatonic theme of the World-Soul, which is at once the macrocosmic equivalent of the individual soul, the Divine Soul, and also the logos or creative force that brings about creation.
"All this serves to make more comprehensible the names, at first sight startling of the seven souls (baw) of the Supreme Being Re: Soul of the Pure Seed; Soul of the Unscathed Flesh; Glorious and Blossoming Soul; Magic-soul; Essence-soul; Male soul; Soul that Copulates."
It would be interesting to compare this with the seven chakras. The Soul that Copulates for example might correspond to the Swadhisthana chakra (associated with the genitals).
From another (macrocosmic) perspective there is in Gnosticism the concept of Aeons or emanations of a Godhead or deity that are both distinct beings and also aspects of the personality of the Deity that emanate them. This is an archetypal theme that reoccurs in Kabbalah as well.
"The ba incarnates itself; it defines the character and affinities of the individual, "each according to its nature". The word ba has several aspects:
expressed in the plural, baw, it is the cosmic soul, the breath of life in all of nature; symbolized by the ram with horizontal horns, it is the soul animating all those beings who, like Osiris, are subject to cyclic rebirth represented by the human-headed bird (top), it symbolizes the human soul.
"...Many are the texts alluding to reincarnation, either overtly or implicitly through such locutions as "renewal of life" or "repetition of births". This eventuality explains the choice of a migratory bird to designate the ba."
Migration can also refer to the transition from one state of existence or world or plane to another. It is not proven that the ancient Egyptians did have a concept of reincarnation or rebirth, and I am rather sceptical on this point. Pythagoras, who was influenced by the Egyptains, certainly accepted transmigration, but it is much more likely that he got it from India (the teachings being carried along trade routes). This said I will not deny that the Egyptians accepted rebirth (transmigration), simply remain agnostic and an open-minded sceptic (which is perhaps the best approach in this and many other matters). Certainly it is not beyond the bounds of possibility that some Egyptian sects or schools might have had some formulation of physical rebirth.