What will happen to my chocolate chip cookies if I add more or less flour than the recipe calls for?
A general answer, because a concise answer would need an entire recipe.
(all ratios that follow are by weight not volume measures)
Flour gives the cookie structure. The commonly followed ratio is:
Cookie dough = 3 parts flour, 2 parts fat, 1 part sugar
That 3:2:1 ratio results in the most common cookie texture.
Adding more flour give you a hard cookie like: ginger snaps, short bread, etc.
Reducing the flour, like a 1:1:1 flour-fat-sugar will give a drop cookie and often chewy.
I Googled, and found this informative piece How to Invent a Cookie Recipe.
More flour will result in a "breadier" cookie. It will have more structure and be less chewy. Less flour will do the opposite, resulting in a softer, flatter cookie.