I just spent some time browsing Flag Stores (via @gray).
Details on the page above were sourced from a list of sovereign states by date of current flag adoption, where it’s shown that the oldest continuously used national flag is that of Denmark — known as the Dannebrog. The nations in the graphic that existed long before the Dannebrog was introduced were simply using other flag designs. Here are a few alternatives you mightn’t be familiar with.
German imperial banner (14th century)
The French Bourbon flag (1598)
Grand Union flag (1775) — the first national flag of the USA
Something new to me — a third of all flags belong to seven main families, and strangely, quite a lot of countries celebrate national flag day.
Flag Stores, by Ferdio. Quite interesting.