
John G. answered 10/03/19
Flexible tutor with MA in Classics
For the most part, each of Rick Riordan's stories, although existing in the same universe, have minimal effect on each other, beyond occasional crossover moments. For the most part, these remain fairly small: one of the Kanes sees a flying horse over Manhattan near the winter solstice, hinting that it takes place concurrently with The Titan's Curse, while a couple of background "normal" characters (i.e., not magicians) in The Kane Chronicles, in particular classmates of the main characters, are actually demigods from Camp Half Blood.
Aside from these, the only time the two series' interact is in the group of short stories that see the Kane siblings work together with Percy and Annabeth, and of course Percy and Annabeth's appearances in the Magnus Chase stories. In many ways, they typically operate very similarly to the relationship in the MCU between, say, Hawkeye and Dr. Strange outside the Avengers movies: the audience knows they exist in the same universe, and there will an Easter Egg or two, but no true interaction.