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 the dough into 2 pieces and shape each piece into a small rectangle.
Lightly flour a large sheet of parchment paper and place 1 piece of dough on top. Lightly flour top of dough, roll into a large, 1/16-inch thick rectangle, and 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 remaining dough.
Bake in the preheated oven until crackers are golden brown, about 24 minutes, turning halfway through.
Remove from the oven and let cool on a baking rack.
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