In a small bowl, whisk together the balsamic vinegar, olive oil, salt, sugar, black pepper, and cumin until combined.
In a medium bowl, combine the rinsed black beans, drained fire-roasted corn, diced red pepper, seeded and diced jalapeño, and sliced green onions.
Toss the bean and corn mixture with the vinaigrette and stir in the chopped cilantro. Cover and refrigerate if not using immediately.
Preheat the oven to 375°F (190°C). Arrange the 6-inch flour tortillas on a large baking sheet in a single layer.
Bake the tortillas for 8–10 minutes until they are golden and crisp; remove from the oven and let cool slightly.
Top each baked tortilla with shredded lettuce, shredded chicken, shredded cheese, and a generous scoop of the black bean–corn salsa.
Finish with salsa, sour cream, and diced tomatoes as desired, then serve the tostadas immediately.