Heat olive oil in a skillet over medium heat. Add chopped onion, cinnamon, coriander, red pepper flakes, 1/2 teaspoon salt, and black pepper. Cook until soft, about 5 minutes.
Stir in garlic and parsley, cooking for another minute until fragrant. Remove from heat and let cool slightly.
In a large bowl, combine the onion mixture with ground chicken and yogurt. Mix until well combined.
Season with remaining salt and pepper, then shape into 4 even patties.
Cook patties in a nonstick skillet over medium heat for about 5 minutes per side, until fully cooked (internal temp 165–170°F).
Brush the burgers with pomegranate molasses and let rest for 5 minutes.
Assemble the sweet and tangy chicken burgers on toasted buns with lettuce, tomato, cucumber, and red onion.