Walkthrough

Egg: Go out of the castle, and cross the bridge to the east. Then, go north to the Chicken Farm, and find the egg. Pick it up.
Milk: In the chicken farm, there should be a bucket too. Pick it up, and go to the cows. Find a dairy cow, and click on it to milk it.
Flour: Go south of the cows, and cross the bridge to the west. Then, go northwest of Lumbridge, find the wheat farm, and pick some wheat there. Then, go to the top floor in the windmill, use the wheat on the hopper there, and operate it. Go to the ground floor and pick up the floor.
Bring the ingredients to the cook in Lumbridge Castle to get your reward and complete the quest.