For the fajita mix: Mix the chili powder, cumin, garlic powder, sugar, salt, red pepper flakes and black pepper in a bowl.
For the salad: Heat a grill or grill pan over medium-high heat and brush with olive oil.
Sprinkle a third of the fajita mix over one side of the chicken breasts. Place the chicken seasoned-side down on the grill and sprinkle another third of the fajita mix over the top of the chicken. Grill the chicken until cooked through, about 5 minutes per side; this will depend on the size of the breasts. Remove the chicken to a baking sheet to cool.
While the chicken is cooling, add 2 tablespoons olive oil and the remaining fajita mix to a large mixing bowl and whisk together. Add the peppers and toss to coat. Place the peppers on the grill and cook, turning to get good grill marks, about 3 minutes per side. Remove to the baking sheet to cool.
Brush the corn with the last 2 tablespoons olive oil. Arrange the corn on the grill and cook, turning frequently, until cooked and brown, about 10 minutes total. Remove to a plate to cool.
Slice the chicken crosswise but keep the slices together. Slice the avocado crosswise, keeping the slices together like the chicken. Squeeze a bit of lime juice over top to prevent the slices from browning.
For the cilantro lime dressing: Add the olive oil, cilantro, lime zest and juice, salt and chili flakes to a mason jar and shake until emulsified.
For the assembly: Arrange the lettuce leaves on a large board or platter. Cluster the chicken breast slices, avocado slices and peppers among the leaves. Tuck in the corn cobs here and there and do the same with the sprigs of cilantro. It should look more free-form than composed. Add the tomatoes, limes halves and chunks of cheese in the same way. Drizzle a bit of dressing over the salad to give it a hint of flavor and serve the rest on the side.