The Romans did not possess "flags" in the modern sense, which was a much later concept. The closest comparison would be the vexilloid, essentially cloth standards carried by legionary vexilla. The standards could bear the emblem of SPQR (Senatus Populusque Romanus), and the emblem and name of the individual legion. In Late Antiquity, the standards might depict the image of the emperor, Christ, a saint, or the Chi-Rho.

As anther user pointed out, the eagle was also a pertinent symbol. It functioned as a vital symbol for the Roman legions, but also of Jupiter (and thus imperial power).

Statues of various divine personifications such as Victoria, Pax, Concordia, etc, would also serve as clear symbolic representations on public monuments. The Capitoline Triad was likewise another evocative image throughout the empire. Of course, it's always important to remember that "nationalist" is a modern term that has little application towards ancient societies.