A little southwest of the Campagna church area and across the Centro border, you'll find a large, enclosed alleyway. The flag's sitting on an overhanging beam.
The next flag is a few blocks southeast of Flag 1, on a beam in an atrium, just above a doctor's shop.
After grabbing Flag 2, head north for a few blocks and you'll find the next flag on a beam above the street, just a little east of the Mausoleo di Augusto.
Head northeast from where you found Flag 3, and the next flag can be found on a vine-covered awning-thing facing the border with Campagna.
The next flag's on a beam in an alley just south of Santa Maria dei Miracoli (which apparently wasn't even built until the late 17th century, but it's not like we haven't put up with worse anachronisms in games before).
You can find the next flag on a beam overlooking the waterfront, due east of the Piazza del Popolo.
Head south along the waterfront from where you found Flag 6, and you'll soon see the next banner on one of those awning-things, next to a ladder.
Keep heading south from Flag 7 until you're west of the Mausoleo and just a bit southwest of the waterfront tailor shop. The next flag is hidden on a beam between a couple of picture windows, overlooking a small ledge.
After grabbing Flag 8, head a few blocks southwest, and you'll find the next flag on an archway over an alley, just west of a church and a doctor's stand.
A little northwest of Flag 9, you'll find a secluded alleyway with rather elaborate-looking architecture. The next flag's on a beam overlooking it.
The next flag's on the roof of the Rosa in Fiore, in the central rooftop-balcony thing.
Southeast of the Rosa in Fiore, there's a courtyard with a tall alcove at its east end. Climb up near the top of the alcove, and you'll find the next flag on a high beam.
The next one's just across the street from the Pantheon, on top of a cross-shaped roof ornament.
Next page: Centro flags 14-26 and feathers 1-4!