The method presented in the book should be a good match for kids, you don't want it to be too complex. The main thing they're going to be struggling with at first is vocabulary. Keep them on picture cards for a while; they're going to be getting a ton of grammar input in school as they try and use the words they know to get by.
One tricky part early on, will be figuring out whether to use a Leitner box (which tends to be a bit more kid friendly) or Anki (which may be more appealing to kids who really like using computers). If they really understand how to teach themselves information in this way, the bonus is they'll be able to use it for all of their other subjects. (We might recommend this article for a broader sense of what skills you want to be training them on: https://fluent-forever.com/create-better-flashcards/)
Note: This article references the Fluent Forever method in general and not the Fluent Forever app. The Fluent Forever app is not suitable or recommended for children.