They can be obtained from Dwarven Powder Keg Stations, which hold an unlimited supply of them, and also from Budger Blackpowder during The Forge Heart quest and in Drakkar Lake after paying him. They are also found in Ancestral Lands and Kaanai Canyon at Alliance Battle shrines; these kegs are used to destroy the gates into the fort.
Powder Kegs are "bundles": this means they have to be carried by hand. When dropped, they will explode after a short fuse time of about 3 seconds. Any enemies caught in the blast radius will be knocked down and set on fire for 3 seconds.