Preheat the grill to medium-high heat.
In a medium bowl, combine the chicken, 2 tablespoons olive oil, and 1 tablespoon taco seasoning; toss to coat evenly.
Grill the chicken 6 to 7 minutes per side, or until cooked through and internal temperature reaches 165°F (74°C). Remove and let rest 5 minutes, then slice into strips.
Meanwhile, make the Tex‑Mex sauce: in a bowl, whisk together 1/2 cup ketchup, 1 tablespoon taco seasoning, 2 teaspoons brown sugar, 1 teaspoon smoked paprika, 1 teaspoon chipotle in adobo, 3 tablespoons chopped cilantro, and the juice of 1/2 lime; season with salt and pepper to taste.
Warm the tortillas in the microwave 20–30 seconds or briefly in a hot skillet until pliable.
Assemble each wrap: lay a warmed tortilla flat, place a layer of spinach toward one end, top with about 1/4 cup cooked quinoa, and drizzle a few tablespoons of the Tex‑Mex sauce over the quinoa.
Add one quarter of the sliced grilled chicken, a few slices of red pepper and avocado, sprinkle with 1 ounce grated cheddar, and add some fresh cilantro leaves.
Fold the sides over the filling and roll the tortilla tightly from the filled end to enclose.
Place the wraps on the preheated grill and cook 2 minutes per side, until lightly charred and warmed through; remove and cut in half if desired.
Serve the wraps with remaining Tex‑Mex sauce for dipping.