I can't remember does Kryptonite work on Doomsday in the comic story?
No, it doesn´t. Since Doomsday was originally SOME Baby and not kryptonian. His original form was bought/aquired/call it what you want from this mad scientiest; Bertron and then being sent out to prehistoric Krypton and being ripped to shreds by it´s inhabiting creatures, remains were collected, cloned and the cycle began anew.
First every form of death worked on Doomsday, but after those thousands to tens of thousands of times cloning, the evolving factor kicked it. So even IF Kryptonite would´ve worked...it would have done so ONE. TIME. Afterwards it would´ve meant pain, but not death.
So if Doomsday from BvS is anything like the comic version and Snyder keeps his words, about exploring him and myths more then that was it.
Kryptonite spear was a one of and since it´s drawing from "the death of superman", then BOTH survived, with Doomsday only being in his "evolving stasis" and Superman truly dead for a time.