What is the study of flags called?
The study of flags is called vexillology. The word combines the Latin vexillum, a kind of flag carried by Roman soldiers, with the Greek suffix -logia, meaning study. Whitney Smith, an American flag scholar, came up with the term in 1957. Designing flags is called vexillography.
Smith was 17 at the time, and the word did not appear in print until 1959. He went on to co-found the North American Vexillological Association in 1967 and designed the national flag of Guyana. Someone who studies flags is a vexillologist.
Vexillology covers the history, symbolism and use of flags. Vexillography is the design side, which is where NAVA's guidelines on what makes a good flag come in. The glossary has entries for vexillology and the Roman vexillum. If you want to try the design side yourself, the flag maker is free and runs in your browser.