Preheat oven to 200°F. Heat 2 tbsp. oil in medium skillet over medium- high heat. Add onions and garlic; cook, stirring occasionally, until onions are translucent, about 10 minutes. Add tomato sauce; pour water into empty tomato sauce can and swirl before adding to pan; bring to boil. Reduce heat to medium low; simmer, stirring occasionally, until sauce thickens slightly, about 2-3 minutes. Stir shredded chicken and cilantro into skillet; cook, stirring to coat chicken in sauce until mixture is warmed through; season with Adobo; remove from heat and set aside.
Heat remaining vegetable oil in medium skillet over medium-high heat until hot, but not smoking. Cook the tortillas quickly, one at a time, submerging completely in oil, until soft and pliable, but not crisp, about 5 seconds each; drain on paper towel.
To form flautas, spoon about 1½ tbsp. chicken filling into center of tortilla; roll tightly to enclose filling, making cigar shape. Secure seam side of tortilla with toothpick. Repeat with remaining tortillas and chicken to make 16 flautas.
Reheat oil in skillet. Add prepared flautas to skillet seam side down, adding only as many as fit comfortably in pan without touching. Cook, flipping occasionally, until browned and crispy on all sides; about 5 minutes. Transfer to baking pan and keep warm in oven until remaining flautas are cooked.
To serve, arrange shredded lettuce on serving platter; top with flautas. Drizzle with crema and sprinkle with cheese.