What would cause a flushed face. No other symptoms.?

Facial flushing. Facial flushing can be due to intense emtions, such as anger or embrassment. Too much alcohol, caffeine, medicaions, including niacin, can cause it too. Medical conditions such as emphysema, carcinoid syndrome and mastocytosis can do that to you. If it’s happening without any identifiable causes, it would be a good idea to get checked by a doctor.
Rosacea. Agree with Dr. A. One other issue to examine would be if you have rosacea. You may visit this site for info: https://www.mayoclinic.org/diseases-conditions/rosacea/symptoms-causes/syc-20353815.