Perhaps you might clarify what you have in mind about Roman flags/banners? The Romans did use military standards (vexilla) but otherwise had no "national flag" (which is essentially a modern phenomenon).

For the Carthaginians, we find depictions of what are apparently naval standards on a third-century (?) stele (see here) and on various coins from the fifth to third centuries. A modern reconstruction is reproduced on the front cover of J. F. Lazenby's Hannibal's War (Norman: University of Oklahoma Press, 1978); somewhat misleadingly, the image shows a cavalryman carrying the standard. In addition, according to the first-century A.D. writer Frontinus, Marcus Porcius Cato once used standards (insignes) captured from Carthaginian ships in an act of military subterfuge (Strategamata 4.7.12).

I am unaware of any evidence that the Barcids possessed their own symbols or standards.

Hope this helps! :)

Sources and further reading: Colette Picard, "Thèmes hellénistiques sur les stèles de Carthage," Antiquités Africaines 1 (1967): 9-30 (photo of the stele on pl. X); Louis Rawlings, "The Carthaginian Navy: Questions and Assumptions," in New Perspectives on Ancient Warfare, ed. Garret G. Fagan and Matthew Trundle (Leiden and Boston: Brill, 2010), 253-87 (esp. 281).

In what way did rome use flags and banners ?