Did people look upon the roman flag (which I'm aware did't function as one in the traditional sense) with pride? Did they see themselves as of the mighty roman empire, or simply under it? Also, was there any music that was seen as expressing the roman identity. Patriotic music, like the British might see Jerusalem or I vow to thee my country, or the Americans the star spangled banner.
There was poetry, namely Aeneid by Virgil, that was commissioned by the Roman government to foster a sense of Roman pride and national Identity. It told the story of Aeneas, a hero from the Trojan war who sailed around the Mediterranean before arriving in Italy and founding Rome. It was basically propaganda that made the Romans seem very justified in their early conflicts, and drew parallels between the past and "present" ~25 BC.
For example, Aeneas landed in North Africa and Dido, queen of Carthage met and fell in love with him. He knew how she felt, but left anyway because he knew it was his fate to found Rome, and Dido killed herself after he left. As a result, the Carthaginian successors and people grew to hate the early Roman republic. The story is likely entirely fiction, but it provided a reason for the Punic wars and conquest of North Africa. It also was a metaphor for Marc Antony and Cleopatra, and the conquest of Egypt. Aeneid is perhaps the best known example of Roman propaganda but there were others.