Combine tomatoes, corn, black beans, roasted peppers, basil, lime juice, garlic, red pepper flakes, salt, and pepper in a large bowl. Toss until thoroughly mixed.
Lay wraps on a work surface. Divide roast beef or turkey evenly down the center of the four wraps and sprinkle each with 1/3 cup cucumber. Top with 1/2 to 3/4 cup of the tomato-corn mixture. Fold the wrap around the filling, burrito-style. Slice each wrap in half and serve with extra salsa.