Make the chimichurri dressing: place the garlic, cilantro, parsley, lemon juice, olive oil, kosher salt, and crushed red pepper in a food processor and pulse until finely chopped and combined.
Taste the dressing and adjust seasoning if needed; set aside.
Combine the shredded chicken, arugula, shredded carrot, chopped cucumber, pomegranate seeds, feta, and chopped almonds in a large bowl.
Toss the salad to mix, then divide among four serving bowls.
Drizzle about 1 to 2 tablespoons of the chimichurri dressing over each serving and serve immediately.