Thought I start out making guides for the easiest quest.
Step oneTalk to the Cook in Lumbridge castle's kitchen.
He will tell you that the duke's birthday is coming up and he forgot to get the supplies for the cake! (What an air head) He will tell you he needs a Large egg, super fine flour, and some world class milk.
Step TwoFrom the kitchen, head outside and across the bridge. Go to the cow pin where all the low levels kill the cows. Talk to Gillie Groats about using her cow.
After some talking she'll allow you to milk it. The cow is located to the east of her. There is a bucket spawn next to the cow
Step ThreeHead to Farmer Fred's house. It is across the bridge from the cows and folow the path. He will allow you to have one of his big eggs after you tell him if for the duke's birthday.
The egg is located just out side his house.
Step FourFrom the farm, go north west, pick some wheat and head into the mill. Talk to Millie Miller about her making the mill make super fine flour. There is a pot located on the table on the same floor with Millie, after talking to her, just climb up the ladders until your on the top floor. Use the flour on the hopper and operate the levers. Head back down the ladder and claim your flour.
Step FiveFinally, Head back to the cook and quest complete! Congratulations!