There are two critical steps in prepping kitchen walls.
Clean and degloss
Cleaning is critical: TSP or TSP substitute.
Deglossing: either light sanding (120 grit) or a chemical deglosser
Once a surface is deglossed, it should be primed, especially if going from one paint type to another.
A deglossed oil undercoat can be primed with a latex primer. Either oil or latex can then be used as a topcoat.
A deglossed oil undercoat can be primed with a oil primer. Either oil or latex can then be used as a topcoat.
It is better to stick within families of paint types, if you can, but going back and forth between types is possible with primers.
At this stage in coating, I'd let everything dry for a week, then sand lightly. If the previous layers are adhering, then proceed with latex primer, latex topcoat.
If,, however, they are sloughing or chipping or you can easily pull a layer off if you leave painters tape on overnight (and then pull it off), then you must sand down to the last well adhered layer and then repaint. Good luck.
I have used oil based indoor paints many times outdoors. Mainly on sheds. The only issue I have had with it is an extreme amount of discoloration. Bright blue turned to really dull pool liner blue, off white turned to dirty-light-yellow.
Honestly I would leave it be for now. If you painted over other latex it might just fall off once it fully hardens and hits a few temp changes. That will make scraping it easier. If it doesn't fall off then just see what happens. It isn't hurting anything.
Best Answer
Sure, I don't see why not. I would even consider doing that with epoxy or LPU, which will clean off much better. The way an average Joe gets brush/rollable 2-part epoxy paint (without going to a chandlery) is garage floor paint.