The Flak skillshot is achieved by destroying a Vulture Gyrocopter with an indirect explosion. Therefore it must be the splash damage from an explosion, not something that has directly hit the Gyrocopter.
During Act 1 Chapter 2 in the Skull camp there is a Gyrocopter in front of several explosive barrels. Underneath the barrels are five Skulls. Shooting the barrels awards you the Flak skillshot plus a five times Enviro Mental skillshot.
You can also achieve this skillshot with the Head Hunter's charged shot. After firing a charged bullet at a Gyrocopter, you can detonate the bullet before it hits it. If it's close enough, the splash damage will destroy the copter.
- This skillshot is named after the real-life Flak cannons used in WWI to shoot down enemy aircraft passing over airfields. Flak was a type of shrapnel loaded into repeating cannons.