The oldest, continuously used national flag is that of Denmark. The current design of a white Scandinavian cross on a red background was adopted in 1625 and its square shape in 1748. In Denmark, it is known as the 'Dannebrog' or 'Danish cloth'.
Although Denmark was never part of the Roman Empire, similar designs were used by the Empire to represent provinces, as the white cross is symbolic of Christianity. The Scandinavian cross has its horizontal stripe slightly to the left hand side of the square as you face it.
Although there is no prescribed definition of what constitutes “continuous" use, the Danish flag was certainly in use in the 1370s, as the Gelre Armorial by Claes Heinenzoon (or Heynen 1345-1414) shows. It was also certainly used in the naval battles during the war against Sweden in the 1560s, as shown in watercolour in Rudolf Dewenter’s Bericht von Pulver und Feuerwerken from 1585. In his War Articles, promulgated on 8 May 1625, King Christian IV issued the first known regulations for flying the flag and Colours of Command in the Navy in Denmark.