Phlegm or mucous is a natural process of mucous production.
If there are irritants or infections, more phlegm may be produced. Clearing this is usually by coughing or blowing. With a baby, excess mucous usually can only be coughed up by the babe. Otherwise you can use a suction bulb to help remove from the nose and back of the mouth. Usually nature will take the proper course & you do nothing.