Well, I don't have a ton of experience with AP Kog, but I typically tend to play squishy, immobile mages mid that scale well into lategame (like Karthus) so I can try to give my two cents as accurately as possible.
Case in point, don't push the wave with your skills; only do it when the wave is approaching your tower and you have to fight it for your own CS. You need to be really passive until mid-game, because early AP Kog isn't really a threat.
The other thing you have to know is that you can't just pick AP Kog midlane without knowing their own mid. Kog is countered hard by mobile assassins which are still popular right now, so only lock him in after you're sure you know that you can survive (somewhat) safely against their pick.
You shouldn't even be annoyed if they take your tower, so you may have to let your jungler know that mid might fall early, but with your great waveclear, it won't be much of an issue in mid-game.
Oh, and one last thing. Exhaust. I don't know what spell you're complimenting Flash with, but Exhaust is underrated. Heal won't save you, neither will Barrier. What WILL sometimes save you is being able to neuter your opponent as they try to kill you, and you fight back with all of your own damage (also a great time for the jungler to show up to help). It's very useful for both assassins and their ADC if they're close enough to shoot you in a brawl or teamfight.
