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.
Painting over a glossy oil paint is indeed different than painting over an oil primer. I just came from a customers's home where the seller did the former - you can literally pull sheets of the paint off the trim. Maybe there are better latex paints that tend to adhere more strongly and you can get away with putting them over oil, but I'd never do it.
Don't take the chance. Either stick with oil-based paint on trim that already has it, or sand and prime first before switching to latex.
Best Answer
Using a primer sealer will help, with that said without texture being applied unless the wall was smooth it will always look different, a photo of the area would help provide a better answer.