This quote relates to the problem of criticising someone (or not complimenting them) when they have power over you (as the King does). How does Cornelia keep quiet on her love for her father, even though she knows she is going to be punished for it, how does the Earl of Kent stick up for Cornelia, knowing he's going to be punished for it. In a way, its even more a criticism of King Lear for he "yields to flattery." From that part of the quote, you can tell that he's an insecure man who needs constant reminders of how great he is. Look at the word "duty" in the quote, it is compelled of those around him to compliment him. He even wants them from his own daughters.