Preheat oven to 425°F. Place turkey wings on a wire rack set on a sheet pan. Bake at 425°F until well browned and crisp, about 1 hour.
Transfer wings to a large Dutch oven. Add stock, onion, carrot, celery, and garlic; bring to a boil over high. Reduce heat to low, and simmer until reduced by half, about 1 hour. Pour liquid through a fine wire-mesh strainer into a bowl; discard solids. Return liquid to pan; bring to a boil.
Whisk together flour and 1/2 cup water in a bowl; whisk into stock mixture until combined. Boil until thickened, about 5 minutes. Stir in salt; serve immediately.