As of now, the question of who is Kiri's father in the Avatar films remains officially unanswered. In Avatar: The Way of Water, James Cameron deliberately leaves it a mystery, creating room for speculation and theories.
However, the film presents clear hints that Kiri may be the child of Pandora’s goddess — Eywa. Such a development would be logical from a mythological standpoint, as Kiri shows a supernatural connection to the nature of Pandora. She doesn’t just feel Eywa’s breath — she literally hears her voice, communicates with plants and animals, and possesses unique abilities, such as the power to breathe underwater longer than others.
This theory echoes the story of Jesus Christ and perhabs Cameron using this symbolism to highlight Kiri’s special mission — to save Pandora and unite the Na’vi and human worlds.

There’s also another version suggesting that Kiri’s biological father could be the scientist Norm Spellman or someone from the Avatar program, but this seems unlikely to be true.
It appears that the answer to this question will become key in Avatar: Fire and Ash and other sequels. Cameron has already hinted that Kiri’s story and her connection to Eywa will be one of the central themes of the upcoming films.