Pour 1 tablespoon soy sauce into a shallow dish. Place 1 tablespoon flour into a separate shallow dish. Toss chicken pieces in soy sauce, then in flour, coating pieces evenly.

Heat oil in a large skillet over medium-high heat. Add chicken; cook and stir until browned, about 5 minutes. Transfer chicken to a plate; set aside.

Reduce heat to medium and stir in curry paste. Cook for 1 minute until fragrant. Add green onions, garlic, and ginger; cook an additional 2 minutes.

Return chicken to the skillet, stirring to coat with curry paste. Stir in coconut milk, sugar, fish sauce, and remaining 1 tablespoon soy sauce; simmer over medium heat until chicken is tender and cooked through, about 20 minutes. Serve curry with cilantro leaves.