Trim the ends from the zucchini. Halve lengthwise, then cut crosswise into 1/4-inch-thick slices (about 2 cups). Place in a large bowl, season with 1/2 teaspoon of the kosher salt and 1/4 teaspoon of the black pepper, and toss to combine.
Remove the husk and silk from the corn. Cut the kernels off of the ears (about 2 1/4 cups).
Finely grate the zest of the lemon (about 1 tablespoon) into a medium bowl. Halve the zested lemon and reserve for later. Add 1/2 teaspoon of the kosher salt, 1 teaspoon of the garlic powder, 3/4 teaspoon regular or smoked paprika, and 1/2 teaspoon of the black pepper. Stir to combine. Cut the chicken breasts crosswise into 1/2-inch-thick strips, add to the bowl, and toss to coat in the seasoning mixture.
Heat the olive oil in a large skillet over medium-high heat until shimmering. Add the chicken in a single layer (it’s OK if the chicken is snugly arranged, but cook in batches if the pan is too crowded). Cook undisturbed until browned on the bottom and it easily releases from the pan, about 3 minutes. Flip the chicken and cook until the second side is golden-brown and an instant-read thermometer inserted into the thickest part registers at least 165°F, 2 to 3 minutes. Meanwhile, pat the zucchini dry with paper towels.
Transfer the chicken to a plate. Add the zucchini to the skillet and spread into an even layer. Cook, stirring occasionally, until browned and tender, 2 to 3 minutes. Add the corn, butter, remaining 1/2 teaspoon garlic powder, 1/4 teaspoon kosher salt, and 1/4 teaspoon black pepper. Cook until the kernels pop and are tender and browned, 3 to 4 minutes.
Return the chicken and any accumulated juices on the plate to the skillet. Squeeze the juice from one of the reserved lemon halves into the pan and toss to combine. Top with torn fresh basil or parsley leaves if desired.