Yes, apples might cause phlegm production. Phlegm is secreted as a consequence of mucus hypersecretion. Apple-related allergies can be a trigger since allergic reactions induce the production of histamine which is a potent vasodilator and it increases secretion of the mucous gland and overproduction of mucous, which in turn causes phlegm production. Another possible cause is the backflow of stomach contents into the mouth.