Sleeping on your stomach will not make the chest flat, but it may affect breathing and reduce sleep quality.
Female mammary gland is composed of glandular connective tissue, subcutaneous fat tissue, etc., by the breast suspensory ligament as well as fascial tissue to maintain the shape of the mammary gland, these tissues have toughness, simply lying on the stomach to sleep squeeze, is not going to make the mammary gland flattened, do not need to worry too much.
Due to sleep on the stomach, may affect the chest rise and fall, a certain range of restriction of breathing, sleep state breathing is not smooth, so that the sleep process is more fatigue, reduce the quality of sleep.
Although the sleep position has little effect on the chest, but may affect the breathing during sleep, try to avoid sleeping on your stomach, usually sleep can take the supine or side position.