Combine chicken stock and agar-agar flakes in a saucepan over low heat; cook and stir until agar-agar is dissolved, 1 to 2 minutes. Refrigerate and chill and until set, 15 to 30 minutes.
Slightly smash ginger with the blade of a broad knife to bring out flavor. Place ginger and spring onion in 3/4 cup warm water in a bowl; rub with your fingers to extract the flavor of the ginger and onion into the water. The water will turn slightly green. Drain and let water cool.
Mix chicken, soy sauce, cooking wine, sesame oil, sugar, and black pepper together in a bowl. Gradually mix in the cooled ginger-spring onion water.
Mince the agar mixture and stir into chicken mixture. Cover and chill in the refrigerator for at least 4 hours.
Place flour in a large bowl; stir in 2/3 cup warm water and vegetable oil. Mix until a smooth dough forms; cover with plastic wrap and let stand for 10 minutes. Cut dough into small pieces and roll into balls; flatten into rounds that are slightly thicker in the center.
Spoon chicken mixture into the center of each piece of dough. Draw up the sides to form a bag shape and twist to seal.
Place in a bamboo steamer. Steam in a skillet filled with about 1 inch of water over high heat until chicken is no longer pink in the center, 10 to 15 minutes.