Vexillology
Vexillology is the study of flags.  The word comes from both the Latin word vexilla "little sail" for flag plus the Greek suffix-ology that means "study of".  The vexillum was a particular kind of flag used by the Roman legions.  Vexillology is a kind of study of symbols related to heraldry.  A person who studies flags is a vexillologist, and a person who designs flags is a vexillographer.