I usually do that when cooking instant noodles. I add an egg to thicken it and it gives additional flavor to the soup.

I'm not sure about flour. I use cornstarch to thicken the broth in making chopsuey.

Cornstarch is the same as cornflour. I typically use that to thicken up gravy too. I see in Food Network that most of the cooks there use all-purpose flour as the thickening agent.

There is a Chinese soup called "Egg Soup"

Beaten eggs can be added to any soup flavored with pork, chicken, crab, shrimp, or even just vegetables. The trick is to gently pour the beaten eggs into the soup and use a fork to stir the in one direction until the eggs form thin streams or ribbons.

It's interesting that you use eggs to thicken broth. I thought you'd use flour?