Combine spices and 2 teas. of salt and sprinkle evenly over chicken breasts. Heat 2 Tbl. oil in a medium sauté pan over medium-high heat, and add chicken, sliced onion, and 1 clove garlic. Cook until the chicken is browned and no longer pink in the center, about 8 minutes per side. Transfer the chicken, onion and garlic to a medium bowl and allow to cool until able to handle.
While the chicken rests, make the salsa roja; Puree the chopped onion, remaining garlic, tomatoes, jalapeño, and cilantro in a blender until smooth, about one minute. Add 1 Tlb. of oil to the sauté pan and heat tomato mixture until slightly thickened and reduced to two cups, about 18-20 minutes. Season the mixture to taste and transfer salsa to a serving bowl, reserving 1/3 cup.
Using your fingers, shred the cooled chicken, and toss with the reserved salsa and the crumbled cotija, mixing well. Season with salt to taste and set aside.
Preheat oven to 435^, with racks in upper and lower thirds, and line two 10x15 inch rimmed baking trays with foil. Wipe out saute pan and add remaining oil. Fry tortillas one at a time for 2-3 seconds per side until just soft; remove from oil and place on one of the prepared trays in sets of four. Place 2 Tbs. filling in a vertical line down the center of each softened tortilla, and roll up tightly.Place seam-side down on the second tray, leaving 2 inches of space between each flauta. Repeat with remaining tortillas, arranging half on each tray. Bake 30-35 minutes, alternating racks and rotating trays halfway through cooking time until flautas are crisp and deep golden. Serve warm with salsa roja on the side.