Kipling uses 'thee and thou' to indicate that the conversation would have been in an Indian language which has a second person singular.
Like many other languages, English used to have a second person singular which was used in speaking to intimates and to people considered to be of lower status (and, strangely, to God). Gradually, we began to use the form 'you' for everyone. However, the King James Bible and the Book of Common Prayer, which both use 'thee and thou', remained in use from the 17th to the mid-20th century, when they began to be replaced by modern language versions.