Melt 1 tablespoon butter in a skillet over medium heat. Add the diced apples, brown sugar, 1 teaspoon cinnamon, lemon juice, and salt. Cook 5–6 minutes, stirring occasionally, until the apples soften.
Whisk the cornstarch with the cold water and stir it into the skillet. Cook 1–2 minutes until thick and glossy. Remove from heat and cool at least 10 minutes.
Stir the granulated sugar and 1 tablespoon cinnamon together in a shallow dish. Set aside.
Spoon about 3 tablespoons of cooled filling down the center of each tortilla, leaving ½ inch clear at each end. Fold in the sides and roll tightly. Place seam side down.
Preheat the air fryer to 400°F for 3 minutes.
Brush the flautas lightly with melted butter. Arrange seam side down in a single layer, not touching, working in batches. Air fry at 400°F for 5 minutes, flip, and cook 4–5 minutes more until deep golden and crisp.
Brush each hot flauta with the remaining melted butter and immediately roll in the cinnamon sugar to coat.
Warm the salted caramel sauce and drizzle over the flautas. Serve warm.