Preheat oven to 400 degrees F (200 degrees C). Spray a baking sheet with baking spray; arrange tofu in a single layer.
Bake tofu in preheated oven until evenly browned, flipping after 10 minutes, about 20 minutes total.
Heat vegetable oil in a wok or large skillet over medium-high heat. Add mushrooms and garlic; cook and stir until mushrooms are tender; 2 to 3 minutes. Add tofu, spinach, soy sauce, and curry powder; cook and stir until spinach is wilted; 3 to 5 minutes. Sprinkle red pepper flakes over mixture.