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.
The first step would be to strip off as much of the old paint as possible. The best way I've found to do this on stucco or concrete is to use a wire brush bit in an electric drill.
Second (and most important), it looks like you have some areas with significant cracks in them, so you'll also want to repair or fill the cracks in order to prevent them from allowing moisture into the stucco. This appears to have been the main contributor to paint failing in the past - note how all of the areas of peeling paint run along the cracks. When the stucco is allowed to absorb moisture, it gradually destroys its bond with the primer.
Finally, use a high quality masonry and stucco primer to ensure a well bonded base coat.
Best Answer
No, in general, you don't need to prime existing paint, but there are exceptions.
To prepare for repainting:
If the cracks are large you might want to check there's not a current movement problem. New houses will settle quite a bit when first built and there'll even be some movement in older homes. If there is current movement then you'll be seeing new cracks appear and older cracks getting longer and/or wider.
If you are painting over a dark colour with a light colour you might need more than 2 coats to stop the previous colour showing through. If that's the case then using a primer or basic white matt emulsion for the first coat (or two if it's really dark) is a more cost effective option than using the more expensive coloured paint for all the coats. Unfortunately you don't always find that out in time.
Paint in full daylight - especially for the final coat - so you can see where you've been and be methodical.