To me, the main conflict in this book is a person vs. himself sort of a conflict. In this book, the main character, Harvey Cheyne, is in conflict with himself as he grows up.
At the beginning of the story, Harvey is a spoiled rich kid. Over the course of the story he has to grow up and become much more mature and responsible. It is very hard for him to overcome his upbringing to do this.
So the story is really a story about Harvey coming of age and becoming a mature and responsible adult.