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.
Alkyd over latex is touch-and-go - well, it works or it doesn't. That depends on several things.
First, is the latex paint new? If it's less than a year old, forget it - it will not be happy being overcoated with an alkyd (oil based) paint.
Second, you can do an adhesion test. If it passes the adhesion test, you are all set - you can use that paint. Google's not much help here because everybody wants to sell you elaborate paint-test equipment. You only need a razor blade, packing tape, and a cotton ball. And this procedure explains it. The test is fairly over-wrought, but you can shortcut down to what matters to you. I've bolded the parts that I'd do.
- Find an area which is concealed and won't show too badly, but is intact.
- Make a cross-hatch of razor cuts through the first few coats of paint.
- Clean it carefully. Don't leave any soap residue.
- Do a tape test: stick tape firmly to the crosshatch area, and pull it off, folding the tape back nearly 180 as you pull it off (not straight out). These first few steps are documented in this video. Also it's better to use packing tape.
- Tape a cotton-ball to the cross-hatched area, and wet it in the paint's reducer (i.e. paint thinner). Use very long runs of tape, as the thinner may try to dissolve the tape goo.
- Wait 30 minutes, remove it and see if the paint has softened or dissolved.
- Wait til it dries.
- Do the tape yank test again.
- Sand, wipedown and prep the crosshatch area same as you plan to prep the house.
- Paint it with that paint.
- Wait til it dries. Look for problems.
- Do the tape yank test again.
Best Answer
You can overcoat over any old paint if these things are true:
Classically one might use TSP (Tri-Sodium Phospate) to attempt to both clean greases and etch the surface.
Where does primer enter the picture?
If you don't have any of those situations, a primer may not be needed.
I am no fan of the Kilz latex primer; I feel the oil-based product is far more suitable for wood. Perhaps the Kilz latex makes sense over drywall; you certainly do need a primer for that.