Make the shredded chicken: To a large pot or Dutch oven, add the chicken thighs, ½ white onion, garlic cloves, bay leaf, 1 tablespoon kosher salt, and enough water to cover the ingredients by 1 inch.
Place the pot on the stove and bring the water to a boil over high heat. Cover, reduce the heat to low, and cook for 10 to 12 minutes or until the chicken reaches an internal temperature of 165°F on an instant-read thermometer. Carefully transfer the cooked chicken to a large mixing bowl and let it rest for 5 minutes or until cool enough to handle. Shred with your hands or a fork.
Heat 1 tablespoon of oil in a small skillet or pot over medium-high heat. Add the tomatoes, jalapeño, and the remaining diced onion and cook for 5 minutes, stirring occasionally, until the onion has softened and the tomato has somewhat reduced.
Pour the cooked tomato mixture on top of the shredded chicken and stir to combine. Taste and season with more salt as needed.
Prepare the frying oil: Fill a large sauté pan or deep skillet with about 2 inches of oil and heat over medium-high heat until the temperature reaches 350°F. (To test, drop a small piece of tortilla in the oil. If it sizzles, it's ready.)
Prep the tortillas: Wrap the corn tortillas in a damp paper towel and heat them in the microwave for 1-2 minutes, flipping the tortillas halfway through until all of them are warm and pliable. Place them in a tortilla warmer or wrap them in a clean kitchen towel to keep them warm during assembly.
Assemble: Place a heaping spoonful of the shredded chicken onto each tortilla. Tightly roll up each tortilla and secure it closed by threading a toothpick along the seam.
Fry: Cooking in batches, carefully add 3 to 4 flautas into the frying oil and fry for 1 ½ to 2 minutes per side until golden brown. Transfer them to a large plate or baking sheet lined with paper towels to soak up any excess oil.
Serve: Remove the toothpicks from the flautas and serve on plates topped with shredded lettuce, salsa verde, salsa roja or hot sauce, guacamole or diced avocados, and crumbled cotija cheese or queso fresco.
Video
Notes
Chicken: To save time, you can shred a store-bought rotisserie chicken instead of making your own or using any leftover chicken you have in the fridge.
Oil: Any oil that is great for frying works. Canola, avocado, corn, or vegetable are all great options.