Flat character is a term used to describe characters that doesn't change throughout the story, and that are not complicated; flat character is the opposite of round character (a complex character that changes over time).
King Hrothgar in the epic story Beowulf, is considered a flat character because when the story is being told, he is an old King. Hrothgar has already lived and reached maturity so he doesn't change or develop and he is not complicated, the only thing complicated about King Hrothgar is that he doesn't have a successor ready to take the throne (and that complication is not directly related to the character's attributes).