If you are using wooden skewers, place them in a container with water to cover for 30 minutes. Preheat the grill to medium high.
For the dressing, in a small bowl or container combine 2 tablespoons olive oil, the lime zest and juice, orange juice, red pepper flakes, and salt and pepper. Set aside.
In a medium bowl, toss shrimp with the remaining tablespoon of oil and season with salt and pepper. Thread the shrimp onto skewers.
Carefully oil the grill rack. Grill the shrimp over medium heat until they turn pink and are just cooked through, about 4 minutes in all, turning the shrimp halfway during cooking. Let cool to room temperature and remove the shrimp from the skewers.
In a large shallow serving bowl, combine the tomatoes, onions, and half the cilantro. Add the half of the dressing and toss. Peel and half the avocados, remove the pit, and dice. Add the avocados and cooked shrimp to the bowl and toss gently to combine. Drizzle with the remaining dressing, and sprinkle with the remaining fresh cilantro.
Serve in the bowl, or serve over the arugula on individual plates.
Notes
The size of the skewers you use to grill the shrimp doesn’t matter, since the shrimp get removed from the skewers and added to the salad. If you want to use bigger shrimp for a more dramatic presentation go for it, just add a minute or two more to the cooking time as needed. The shrimp are coated in plain olive oil and salt, which adds a bit of flavor and prevents them from sticking. They will get another boost of flavor from the dressing once the salad is assembled.