Make salad: In a large bowl, toss together chickpeas, cucumber, bell pepper, red onion, olives, and feta. Season with salt and pepper.
Make vinaigrette: In a jar fitted with a lid, combine olive oil, vinegar, lemon juice, parsley, and red pepper flakes. Close the jar and shake until emulsified, then season with salt and pepper.
Dress salad with vinaigrette just before serving.