In a large bowl, whisk dill, mint, lemon juice, and ¼ c. oil; season with salt and black pepper. Add fennel, chickpeas, and olives and toss to combine.
In a large skillet over medium heat, heat 1 tbsp. oil. Add Halloumi and cook, turning occasionally, until charred and golden on both sides, 4 to 6 minutes. Transfer to a large paper towel-lined plate.
In same skillet over medium heat, heat remaining 1 tbsp. oil. Add pita and toast, turning halfway through, until golden and crisp, about 4 minutes. Transfer to plate with Halloumi.
Add arugula, orange, avocado, Halloumi, and pita to bowl with fennel mixture and toss to combine; season with salt, black pepper, and crushed red pepper flakes.
