Pests like cockroach, silverfish, etc., are attracted to damp and dirty places, so ensure your paintings are stored in a clean and dry area, free from moisture, dirt, and soil. You should also store them in airtight storage boxes, preferably made of plastic. Alternatively, you can use insect repellents and seek the services of a professional pest control company.
As such, I do not recommend keeping your paintings in the kitchen, which is more prone to pests, smoke, etc. And if you have a personal art gallery at home, avoid smoking in the area.