Scarlett will need a warhammer or battle ax to destroy the nests.
By far the easiest way to deal with the Flying Beasts is to use the necromantic spell Blood Vortex. With several levels of mastery, Scarlett can destroy the entire flock with one casting. Aeris can teach Scarlett this Mental Skill (or improve her mastery of it), if she didn't already learn it from Nox, assuming she has sufficient Skill Points. Killing the whole flock with a sword is tedious.
Flying Beasts nest in chimneys on rooftops. There are a total of three such Flying Beasts nests on the Inner City Rooftops. Scarlett must destroy all three to complete this quest. (Note that it is not strictly necessary to kill the Flying Beasts themselves; however, they will make it difficult to destroy the nests if left alive.)
Since Scarlett gets the quest from San, it's logical to begin with the nearest nest. Leave San's Occult Shop and walk across the street, entering the nearest house (1). Inside, go upstairs and exit by the window, which will leave Scarlett on the rooftops right near the first nest (1). Kill the Flying Beasts (a Blood Vortex spell is the easiest way), take out a war hammer, and smash the chimney/nest. Go back in the same window, downstairs, and out to the street again.
Head south along the street to a wooden, scaffold-like bridge. Cross the canal there and head north on the other side of the canal on the wooden boardwalk until reaching a ladder (2). Climb the ladder up to the rooftop and head south to the second nest. Again, kill the Flying Beasts and use a war hammer to smash the chimney/nest (2). Now head eastward on the roof, using a makeshift bridge to cross a narrow street to find the third nest (3) and destroy it, too.
Return to San to report success, claim her reward and complete the quest.