Read first, or watch first?
Nothing to decide here, because nothing will spoil anything — these are twelve separate tales with no plot to give away. Watch the Rabbit Ears Elephant's Child whenever you like; it is a fair audition for the book's voice and it rents for a couple of dollars. What it will not do is stand in for the book, because eleven tales, all the verse, and every one of Kipling's captions are outside it. If you want the shortest possible test of whether this book is for your family, read the first page of How the Whale Got His Throat aloud — the one with the starfish and the garfish and the really truly twirly-whirly eel. That page decides it.