Do you avoid the damage if you kill a turret right before its missile hits you?

No, If the missle has been shot, you will take the damage no matter if the turret is there or not.

A shot that acts like a guided missle can not be avoided. Only shots that are not guided can be avoided by stepping or flashing aside.

The turret has a Guided missile system. So that means it will hit you and damage you no matter what you do.

It shouldn't be too easy after all.

A turret is there to give protection. Not to be dodged by every attacker.

The shots already been fired. Just like how skill shot will still hit for a short time after the champions dies, the turret's shot will still go for you.