There’s nothing strange about using archaic language in an archaic story. But Kim was set and published a solid century after thee/thou had fallen completely out of favor. OP wanted to know why Kipling used archaic language in a story that was not set in that archaic period.
That’s a reasonable question, and it did have a reasonable answer, as explored in the rest of the thread. But it’s not just “it uses old language because it’s old.”
Is that the James Patterson, creator of James Patterson’s Bookshots?!?