Weigh or lightly spoon flour into a dry measuring cup. Combine flour, cornmeal, baking powder, 1/2 teaspoon salt, and 1/4 teaspoon pepper in a large bowl.
Combine sour cream, eggs, and 1 tablespoon oil in a bowl, stirring until smooth. Add sour cream mixture, corn, and jalapeño to flour mixture; stir just until combined.
Heat a large nonstick griddle over medium-high heat.
Divide corn mixture into 8 equal portions (about 1/3 cup each); shape into patties. Add patties to griddle; cook 6 minutes on each side.
Combine squash, green onions, basil, vinegar, tomato, remaining 1 tablespoon oil, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper in a bowl; toss. Place 2 corn cakes on each of 4 plates; top evenly with salsa.