The giant dragon appears towards the end of "Food of the Dragon", where it is seen eating Eustace. According to William and his brother (both Water Dragons); Flying Dragons only eat people, while Water Dragons only eat fish.
As stated before, the Flying Dragon appears at the end of Food of the Dragon. When Muriel and Courage are eating food with William and his brother, Eustace is handed a fish popsicle. As he begins to chow down on his snack, a red dragon can be seen flying in the background. The monster begins to roar, which gains Eustace's attention. He begins to scream as the flying dragon swoops down to eat the farmer. The dragon then bites down on Eustace's head and swings him in the air, making him land in the creature's mouth. The dragon roars and flies away, with Eustace yelling "Stupid dragon!" from within the monster's belly.