Preheat the oven to 350°F.
Place the chicken thighs onto a small baking pan. Rub ½ teaspoon taco seasoning into each thigh, coating all the surfaces. Roast, uncovered, for 40 minutes. When cool enough to handle, discard the skin and bones. Coarsely chop the chicken. Set aside.
In a medium skillet, heat 1 tablespoon canola oil. Add the onion; sauté until shiny, 4-5 minutes; do not allow it to brown. Sprinkle in remaining 2 teaspoons taco seasoning, cayenne, and beans. Add the chicken; cook for 3 minutes. Remove the pan from the heat. Stir in the tomatoes and cilantro.
Place ¼ cup of the chicken filling into the center of each tortilla. Roll each tortilla tightly around the filling, securing each flauta with 1-2 toothpicks.
Heat 1 inch canola oil in an 8-quart pot. Using tongs, hold a flauta in the hot oil until firm, then release; cook until golden brown, about 2 minutes. Remove to a paper towel-lined plate. Discard the toothpicks. Repeat with remaining flautas.
In a food processor fitted with the metal “S” blade, pulse the avocado, mayonnaise, and lemon juice until smooth.
Serve 2 flautas per plate, topped with avocado cream and garnished with chopped cilantro.