Dishwashing liquid wont work with spider mites. If you can't get soap flakes, try buying a bar of pure soap, and just grate it up. The purpose of the soap is to destroy the waxy layer on the mites, and that way the poison can be delivered to the mites. The soapy water also sticks to the mites.
You could try the soapy water on its own, but I think you would get a better effect with the alkaloids added to the soapy water.