How do I apply latex paint over oil based paint?
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.