The box of matches can be found by examining the space heater in the middle of the infirmary in the first chapter. It is necessary for Naomi to escape the infirmary after the black mist blocks the door outside with hair. However, Naomi must first douse the hair blocking the door with rubbing alcohol before using a match to burn away the hair, or else it won't be effective.
Yoshiki can pick up the box of matches in the space heater of the science lab, during the scene where the anatomical model is holding Ayumi captive. He must also pick up the gas burner lying next to a table and he will automatically use both against the anatomical model.