There is no real explanation given for why flamingos prefer standing on one leg when resting. However, there are several ideas that have been raised and may help human beings understand why these birds do this.
One of the ideas is that these birds stand on one leg in order to conserve body heat. Since birds lose a lot of heat though their legs, standing on one may help reduce the amount lost. Another idea is that standing on one leg helps prevent muscle fatigue, since one leg is not strained and can help with faster fleeing in case a predator shows up.