Preheat the oven to 350 degrees F (175 degrees C).

Combine flour, sourdough starter discard, olive oil, rosemary, and kosher salt in a bowl. Mix with a wooden spoon to incorporate the ingredients. Turn out onto a work surface and knead until a smooth dough forms. Divide dough into two pieces and shape each piece into a small rectangle.

Lightly flour a large sheet of parchment paper and place one piece of dough on top. Sprinkle dough lightly with flour, then roll into a large, 1/16-inch-thick rectangle. Cut into 1 1/4-inch squares. Spray tops with cooking spray and sprinkle with flaked sea salt. Carefully transfer the parchment paper and dough to a baking sheet. Repeat with the remaining dough.

Bake in the preheated oven until crackers are golden brown, about 24 minutes, turning halfway through.