Giant Kozaky's effect is continuous, so as soon as it has a chance to, it will destroy itself. It can destroy itself between chain links, but not during a card resolution. So if you chain a second
Skill Drain to the activation of a MST or other card destroying your existing
Skill Drain, you will be fine.
In your example above, when you activate
Emergency Provisions, you send
Skill Drain to the graveyard as a cost. If nothing else is chained to the activation of
Emergency Provisions, then
Giant Kozaky will be destroyed after
Emergency Provisions resolves.
However, let's say that you or your opponent chains a trap to this. Let's use something simple like
Jar of Greed.
Jar of Greed will resolve, the the drawing of a card. After Jar resolves, GKs effect kicks in and destroys himself, since it is a continuous effect. However, its damage effect doesn't kick in immediately, because you can't start another chain while one is resolving.
Emergency Provisions would resolve, giving you the Life Point boost, and then GK's damage effect would activate, starting a new chain, in which you could chain Barrell Behind the door or something else.
If I run a fiendish
Skill Drain deck and decide to throw
Giant Kozaky in there, I'll probably make sure to keep an equal number of
Barrel Behind the Door cards in the deck as well to have a backup plan for GK 8^D
Hope all that craziness makes sense. 8^D