A is for Apotheosis

Your purification is the purification of Heru

Your purification is the purification of Set
Your purification is the purification of Djehwty
Your purification is the purification of Dwn-Anwy
Your purification is the purification of your ka
Your purification is the purification of your purification
and this purification of yours also
Is among your brethren, the gods.
- Pyramid Text 36

Your brethren, the gods.

What kinship is there between the human and the divine?

Well, there's the ka, of course, as explicitly mentioned - which is fundamentally the many-divided and multiply-intertwined ka of the Creator, differentiated unto millions.  But the ka is a different sort of identity than is addressed with "you", most times, so that is at best only an incomplete suggestion of an answer.

The word for 'god' in Egyptian can be translated with, I feel, more nuance, as 'divine power'.  And I would suggest from that that there is a gradation there: one can have divine power, and one can also be a divine power.  Certainly, there are cases in Egyptian lore of a human accumulating sufficient netjer to become netjer - Imhotep being a primary example of such a person (who was not previously a bearer of the Kingly Ka, which complicates the whole divinity question a touch).

Heka - the most commonly discussed power of magic - was a gift granted to humans in order to "ward off events", or something rather like that.  It is a divine power.  (It also means 'activation of the ka', and thus resonates with that deep divinity.)  Akhu, another magical word, is also the word for "ancestors", and indeed the ancestors are commonly thought of as closer to the gods in some ways than the living.

But there is the inner truth, the personal netjer, that ideal and aspirational being, the personal power within.  That which you are the only one who can achieve it is bound up with that personal divinity, that personal place.  The intimate and most individual of powers, the purification of which is also the purification of your brethren, the gods.

Who is this flower above me

And what is the work of this god?
I would know myself in all my parts.
- "The Flower Prayer"