I have no real answer for you other than personal experience.
As a child, I was a voracious reader. (Still am.) Apparently, I voraciously read a lot of British work. (Still do.) To this day, I instinctively type the British spelling of a word only to go back and remind myself that I'm an American.
As a parent, I have two boys who are young readers: one is quick to pick up new words and remembers the proper spelling of said words easily, and one who struggles with new words and spellings and letter reversals. There's a series of books that was highly recommended to help boys learn to love reading. I purchased the entire series and my sons have been devouring them. Unfortunately, I discovered that the stories have a lot of intentionally misspelled words. While this is fine for one boy - he's the one who pointed it out to me and explained why the author chose to write that way - the other boy is now further confused about how to properly spell these words.
I guess, the point I'm meandering around here, is that kids definitely learn to spell through reading. Encountering the British spelling of words will enable a discussion about the differences in language for some and righteously confuse others. As a parent, I guess I'd suggest an American version (if it's not too costly for you to create).