I have 2 kitchens, one is for MAX-sec and the other is shared. When I built the second kitchen(Max) the other isn't making food anymore. I was about to make a third kitchen for Med but then I saw this problem and I don't know what to do.
Prior to version alpha-28, the AI of the chefs just couldn't handle multiple kitchens and canteens. However, this was improved a lot in that update.
Usually the AI does an adequate job at figuring this out on its own, but sometimes you need to set this up manually. When you research "Micromanagement" you will be able to set which kitchen supplies which canteen and which cell block eats in which canteen. This feature is found under "Logistics"->"Food Distribution".
When the kitchen still doesn't supply the right canteen, there might be something wrong with either the kitchen or the canteen. Make sure that the room areas are designated as the correct room type, that all required objects are installed and in case of the kitchen that all cookers and fridges have electricity and all sinks have water.