Final answer:
The 'Flame-ware' vessel belongs to the Middle Jomon period, specifically dating from approximately 3500 to 2500 BCE in Japan. During this period, vessels were made using the coil construction method and decorated with cord patterns.
Step-by-step explanation:
The 'Flame-ware' vessel belongs to the Middle Jomon period in Japan.
The Jomon period, which lasted from around 14,500 BCE to 300 BCE, is known for its distinctive pottery with cord patterns.
The Middle Jomon period specifically dates from approximately 3500 to 2500 BCE. During this time, vessels were made using the coil construction method and decorated with cord-marked and incised patterns.