You are going to need a primer because of the gloss and the deep color. There are much better choices than Kilz for primer and paint but if you have the paint, it might work for you after you prime.
You should scruff the gloss surface to give it some tooth for adhesion. I know this sounds like a horrible task but get yourself a reasonable wide pole sander and some fine grit paper and it will go fast. Clean the surface thoroughly and especially if this is in a kitchen or some similar place. TSP from the paint store would be a good bet.
Then apply a high bond primer. An alkyd (Zinsser Cover Stain or Benjamin Moore Fresh Start) might be a wise choice because if it is high gloss and a deep color it most probably is an oil solvent finish. However, if you plan to use latex for the finish coats, a good high bond latex acrylic primer like Zinsser 123 would do the trick.
I would take the Kilz back if you haven't opened the can and get some nice paint store paint.
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