Char peppers over gas burners or in broiler, turning frequently. Transfer to a medium bowl and top with a plate. Let cool slightly. Rub off skins and remove stems and seeds. Set aside.
Meanwhile, soak dates in hot water for 10 minutes until softened. Drain.
Pulse pomegranate seeds in a food processor. Strain liquid, discarding solids. Return to food processor and add roasted peppers, softened dates, walnuts, and red pepper flakes. Process until smooth. Slowly add olive oil. Season to taste with salt and pepper.
Toast pitas over gas burners or in broiler, turning frequently. Drizzle with olive oil and season with salt. Serve warm with dip.