There are two possible reasons why your String of dolphins plant has flat leaves. It is either because you have severely overwatered the plant or the plant is placed in a location where there is a lack of sunlight exposure. You can be the best judge of what scenario applies to your plant.
Ensure to withhold any watering, and only water the plant when the soil appears dry. Moreover, relocate your plant to a spot where it receives adequate sunlight. Adopt both measures for a week, and you will observe your plant regaining its fleshy plump appearance.