Combine first 6 ingredients in a bowl, and set aside.
Combine rice and basil; set aside.
Arrange bell pepper, zucchini, yellow squash, and 1/4 cup red onion in a single layer on a baking sheet. Broil for 12 minutes or until the vegetables are browned; spoon into a large bowl. Drizzle vinegar and oil over vegetables; toss to coat.
Warm tortillas according to package directions. Spoon 1/4 cup of rice mixture down center of each tortilla. Top each with 1/2 cup roasted vegetables, 2 tablespoons tomato mixture, and 1 tablespoon cheese; roll up.