In a large bowl, combine steak, oregano, red pepper flakes, 1 tablespoon olive oil, 1 tablespoon lemon juice, 2 ½ teaspoons garlic, and 1 teaspoon salt. Cover and let marinate at room temperature at least 30 minutes or up to 2 hours, or refrigerate up to 4 hours.
Meanwhile, in a small bowl, combine remaining 1 tablespoon lemon juice and ½ teaspoon garlic; season with a large pinch of salt. Let sit about 20 minutes.
Add tahini, honey, 3 tablespoons olive oil, and 3 tablespoons water to dressing. Vigorously whisk, adding more water as needed, until smooth and easily pourable; season with salt and black pepper. Set aside.
In a medium skillet over medium-high heat, heat 1 tablespoon olive oil. Add orzo and cook, stirring, until golden, 3 to 5 minutes. Add broth and bring to a boil, then reduce heat to medium-low. Simmer, stirring occasionally and adding more broth ¼ cup at a time if needed, until broth is absorbed and orzo is tender, 8 to 10 minutes; season with salt and black pepper. Cover to keep warm.
Prepare a grill for high heat; preheat 5 minutes. Brush grates with neutral oil. Thread 8 skewers with steak, onion, bell pepper, and tomatoes, alternating with 3 to 4 steak cubes per skewer. Drizzle kebabs with remaining 2 tablespoons olive oil; season with salt and black pepper.
Grill skewers, turning occasionally, until vegetables are tender and meat is cooked to desired degree of doneness, 8 to 15 minutes total (grills can vary). Transfer kebabs to a plate.
In a large bowl, toss cucumbers and spinach with half of reserved dressing. Stir chives into orzo mixture.
Divide salad and orzo among bowls; top with kebabs. Drizzle remaining dressing over bowls.