This is the third quest you complete alongside Rhona Dinsmore. To start it, after completing the quest "A Thief in the Market", return near the bureau and speak with Rhona once again to show her the map you managed to obtain.
To cripple Hilary Flint's defenses, Edward must blow up his powder storehouses.
Three locations will be marked on the map containing powder reserves that you must destroy. In each of these locations - all of which are restricted areas guarded by several soldiers - there is a powder keg that you can ignite or destroy from a distance with a well-aimed pistol shot.
The first powder reserve is located slightly north of where you are. Head there by moving across the rooftops. Once you arrive at the location, start by taking out the marksman on the roof.
Next, shoot the red barrel standing in the courtyard with your pistol, and once it explodes, quickly move away to lose aggro.
Move to the second marked location - ideally, keep moving across the rooftops. Once you get there, take out the two marksmen on the roofs. First, eliminate the one patrolling the rooftops after he walks off to the left, and then the second one who remains standing in the same spot the whole time.
From the top of the scaffolding, right next to where the second marksman was standing, you should see the second red keg. Shoot it and move away quickly to lose aggro.
Head to the last location, situated furthest to the north, and take out the marksman patrolling the rooftops of the restricted area.
The powder keg is under a canopy. It is hard to see, but you can easily hit it with your pistol while staying on the roof.
Once all three kegs are destroyed, this quest will end and the next one will unlock - Flint's End.