Whisk eggs, milk, and salt in large bowl until well combined.
Heat 1 tablespoon oil in 12-inch nonstick skillet over medium heat until shimmering.
Add egg mixture and, using rubber spatula, constantly and firmly scrape along bottom and sides of skillet until eggs are just set, 2 to 4 minutes.
Off heat, fold in kale.
Transfer egg mixture to plate and wipe skillet clean with paper towels.
Heat remaining 1 tablespoon oil in now-empty skillet over medium heat until shimmering.
Add scallions, cumin, and chili powder and cook until fragrant, about 1 minute.
Stir in beans and their canning liquid and cook, mashing beans with back of spoon, until mixture is heated through and thickened, 3 to 5 minutes.
Off heat, stir in cilantro and lime juice.
Season with salt and pepper to taste.
Wrap tortillas in damp dish towel and microwave until warm and pliable, about 1 minute.
Lay tortillas on counter and spread bean mixture evenly across each tortilla, close to bottom edge.
Top with egg-kale mixture.
Working with 1 tortilla at a time, fold sides, then bottom of tortilla over filling, then continue to roll tightly into wrap.
Arrange up to 4 burritos, seam side down, in air-fryer basket, spaced evenly apart.
Place basket into air fryer; set temperature to 400 degrees; and cook until crisp, 5 to 8 minutes.
Individually wrap remaining burritos in greased aluminum foil.
Transfer to zipper-lock bags and freeze for up to 2 months.
To bake from frozen, place foil-wrapped burritos into air-fryer basket.
Place basket into air fryer; set temperature to 325 degrees; and cook until heated through, about 30 minutes, flipping burritos halfway through cooking.
Let rest, wrapped in foil, for 5 minutes before serving.
