In a large bowl, combine the red wine vinegar, mustard, thyme, red chile flakes and garlic. Whisk in olive oil and season with salt and pepper to taste. Stir in chickpeas, salami, provolone and mozzarella. Cover and let marinate in the refrigerator until ready to serve or up to an hour.
Just before serving, toss salad with arugula. Scatter the roasted red peppers over top. Season with salt and pepper to taste.