Phosphorus Bomb can be used to reveal enemy units that might be hiding in a nearby patch of brush.
Valkyrie can be used defensively as well, so try using it for a quick escape.
Corki can continue to attack while using Gatling Gun. Maximizing Gatling Gun is key to mastering Corki.
Watch out for Corki's Missile Barrage. They deal splash damage, so you can get hit even when hiding behind minions.
Corki is vulnerable after he uses his Valkyrie, so try switching focus to him if he uses it to enter a fight.