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I would keep on as you are doing. Your dog is used to cats, his cat, I would not expect it to take long for him to realize the new kitten is his cat as well.
Normally you would keep the kitten behind the closed door, as it seems you intended, but that step is over now, unintended but it is, so I don't see a point to going back to it.
Other tricks are feeding and petting in each other's presence. One I always do is make sure the first pet is greeted, petted, fed, spoken to, played with first. I do suspect this makes me feel better but I think it helps reassure the first pet they aren't being replaced.
Good luck. They may not become best buddies but tolerance for each other is acceptable.
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