You can reach Pantelleria island from several airport near Milan: from Linate airport, from Malpensa airport and also from Bergamo Orio al Serio airport.
From Milano Linate there are direct flights every Saturday from end of May to middle October opertated by Volotea. Or with ITA but only in August.
From Bergamo Orio al Serio to Pantelleria there are direct flights with Volotea airline, every Saturday and Sunday, starting from 27th May to October.