You can see the first page of the published sheet music here. It says "Words and music by Marta Keen." It doesn't mention Kipling.

Kipling wrote 39 books from 1886 to 1923 and only 7 books after 1923; therefore most of his work, and all of his well-known work, is in the public domain (at least in the US) and should be fully searchable with Google—but I can't turn up any phrases from HOMEWARD BOUND.