others have said some of these items but i'm just writing my thoughts out as they come to me so there will be some overlap but maybe my thoughts are helpful to you as well, good luck!

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1. 65% RH is probably higher than it should be. First thing to do is get a dehumidifier in there and keep it running so that RH is below 55%.
2. Does the kitchen have an exhaust fan that exits outside? (i'm guessing that it doesn't). Look into installing one but if this isn't possilbe then you'll just need to keep the dehumidifier running all the time
3. is there a bathroom upstairs? there could be some leaking into those walls but a person might expect the paint flaking to be seen everywhere along the wall, not just in those lower locations so this is unlikely
4. most likely, the walls are wicking water up from the ground. Check your downspouts to make sure all water is being pushed far away from the house. Is the ground properly sloping away from the house? Is the back "garden"/patio sloping away from the house? The next time it rains go outside and have a look and see where water is pooling or puddling. If it's in areas close to your house then you need to fix those spots asap.