From Fluffy's point of view, the last thing he cares about is being groomed. Fluffy has no idea what being touched all over by his owner is like and that he is not supposed to become anxious and hard to handle when you try to groom him. Chow Chows do need an owner with a strong will and desire to be the "Alpha" in the pack. When you attain this coveted position in Fluffy's mind, grooming him will be much easier.
One of the most important things you can do to make grooming easier for both you and Fluffy is to start right from the beginning establishing yourself as Alpha. This will help make your fuzzball more likely to obey and submit, which will make the actual grooming sessions go far more smoothly for both of you.