How to Make It
Preheat grill to high (450°F to 500°F). Toss together zucchini, onion, corn, garlic, and 2 teaspoons of the oil in a large bowl. Arrange vegetables in a single layer in a metal grilling basket lightly coated with oil. Place basket on grill grate, and grill, uncovered, turning occasionally, until vegetables are charred, 4 to 6 minutes. Remove from grill. Cut corn kernels from cob; discard cob. Set aside vegetables.
Roll dough into a 14- x 10-inch oval on a lightly floured surface. Place on lightly oiled grates; grill over high heat, uncovered, until lightly browned, about 1 1/2 minutes. Flip over; brush top with remaining 2 teaspoons oil. Top with chicken; sprinkle with cheese, leaving a ½-inch border around dough edges. Arrange vegetables over pizza. Grill, uncovered, until cheese is melted, about 1 1/2 minutes. Remove from grill.
Sprinkle with salt and black pepper; top with basil and red pepper flakes.