This is an interesting question, because actually I would want to argue that there are several conflicts in this great novel. However, if we are trying to identify the "main" conflict, I would say that it would have to be the conflict between Digory and Polly and Digory's uncle, Uncle Andrew. Of course, it is Uncle Andrew himself that uses the children as guinea pigs, sending Polly against her will into another world and then forcing Digory to go after her so she can return. Note how Uncle Andrew is presented in Chapter Two:
"I hope," said Uncle Andrew presently in a very high and mighty voice, just as if he were a perfect Uncle who had given one a handsome tip and some good advice, "I hope, Digory, you are not given to showint the white feather. I should be very sorry to think that anyone of our family had not enough honour and chivalry to go to the aid of--er--a lady in distress."
Uncle Andrew is therefore presented as a manipulative man who uses children to do what he is not brave enough to do himself, and blatantly blackmails Digory into fulfilling his commands without any moral compunctions. It is this conflict between the children and Uncle Andrew that starts the story and leads them on into the other conflicts that they face.