Vexillum
The vexillium(banner) had the closest resemblance to a flag. It was usually a red banner with the number of the unit in roman numerals, an abbreviation of the unit, and sometimes a picture of a god. The flag itself was hung down from the wooden crossbar of the pole that it was carried on. It was used by the infantry when it separated from the rest of the army and it was a common standard for the Praetorian/auxiliary cohort. The vexillium was carried by the vexillarius(flag-bearer) who wore the head of a fox on his head. The vexillium was first used as a standard under Constantine, the first Roman emperor to convert to Christianity and make Christianity the official religion of Rome. Because of this, many Christians use flags in the form of vexillia as symbols of Constantine in churches.
Fun Fact: the word "vexilium" comes from the word velum(sail), so vexilla are meant to be little sails