Grate the zucchini on the large holes of a box grater and transfer to a bowl. Toss with ½ teaspoon salt and let sit for 10 minutes. Squeeze out as much moisture as possible, then transfer back to the bowl.
Add corn, lemon zest, half the scallions, and ¼ teaspoon each salt and pepper and toss to combine. Add egg and mix to combine. In a small bowl, combine the flour and baking powder. Add to the zucchini mixture and mix to combine.
Heat 1 tablespoon oil in a large cast-iron skillet over medium-high heat. Drop 4 spoonfuls of the zucchini mixture (about a scant ⅓ cup each) into the skillet, then use the back of the spoon to gently spread out. Cook until golden brown, 2 to 3 minutes per side; transfer to a rack.
Add 1 tablespoon oil to the skillet and repeat with the remaining zucchini mixture.
In a large bowl, toss the tomatoes with remaining tablespoon oil and ¼ teaspoon each salt and pepper. Toss with the arugula and remaining scallions.
