For the spice rub combine the paprika, cumin, oregano, coriander, crushed red pepper flakes, and kosher salt in a bowl. Place in a sealable jar, keep in a cool dry place for up to 6 months.
Place chicken in a shallow dish. Drizzle with extra-virgin olive oil to barely coat the meat. Rub chicken liberally with 4 tablespoons of the spice blend. Let stand 10 minutes.
Grill chicken 6 or 7 minutes on each side or until juices run clear.
Seed and chop the tomatoes and combine with onion and parsley in a shallow bowl. Combine oil, lemon juice, and spices in a small plastic container with a lid. Shake dressing to combine and pour over salad. Season salad with kosher salt and toss to combine well. Let stand 10 minutes and serve.