Kimolos Cyclades is a tiny island with no big shopping options. There aren't any big commercial stores, of course. You can only find some small and lovely shops that sell the basic products and some gift shops with souvenirs.
The shops of folk art on Kimolos sell embroideries, woven fabrics, ceramics and wooden carved showpieces. Most of these shops are found in Chorio, the capital of the island. Have in mind that shop owners on Kimolos do not accept a credit card, so make sure you have cash with you.