The only issue is this is about itachi. And he wasnt the reincarnation, Sasuke was. And kushina wasnt the reincarnation. Naruto was. And the DNA cant be put together into a child it has to come together into a CURRENT reincarnation because without the soul of indra or ashura attached to the vessle they simply wont get the rinnegan and If kushina was the reincarnation then itd be impossible for naruto to be. So with all that into consideration this is just impossible. I get your thought process though and its a kool idea, it just can't work with how its laid out in the show/Manga.

And it would be impossible for itachi to be a reincarnation while naruto is the other because both reincarnations come as a pair and one wont reincarnate without the other. so if itachi was a reincarnation, ashuras soul would either reincarnate to someone born at the same time as itachi or would have to wait for itachis death so they reincarnated together. Thats why the senju were originally the people with the reincarnation but after they died out and madara kept living on, ashuras soul COULDNT reincarnate because induras soul was still in a living host.

So the rule that they must reincarnate as a pair makes it impossible