2/3 cup plain Greek yogurt
Stir together the yogurt and salt. Combine the chicken, cumin, cinnamon, garlic, and 2 tablespoons of the yogurt mixture in a medium bow. Shape into 8 (3-inch long) oval patties.
Heat the oil in a large skillet over medium. Cook the patties, turning occasionally, until golden brown and cooked through, about 12 minutes.
Stir the water and lemon juice into the remaining yogurt mixture. Toss together the rice and pomegranate seeds. Sere the patties with rice; top with the yogurt sauce and cucumber.