What is the conversion ratio from whole potatoes to potato flakes?
I would aim for the amount of flakes that would make 2 cups of finished mash. Add 1/2 to 2/3 of it and see where you are in terms of thickness of the soup. If the soup is still thin add more.

This also depends on what potato the flakes are made from, any additives to the flakes, etc.

Usually when a recipe is not specific with an agricultural product I assume I have a lot of margin for error.  Cooking requires a lot of experimenting, but using the flakes may actually make your life quite a bit easier here as you can add as much or as little as you want "to taste."