This paper studies on delivery-guaranteed and effective data dissemination for mobile sink groups in wireless sensor networks. A mobile sink group denotes a set of tightly coupled mobile sinks for team collaborations such as a team of firefighters and a group of solders. The mobile sinks have a group movement feature. They thus randomly move in personal spaces as well as collectively move together as a single entity. To support such group mobility, previous studies provide circle-based protocols determining successive circular areas of a group continuously moving, and then propagate data in the areas by flooding. However, since a group is still moving during decision of each circle, they may cause asynchrony between circles and actual group positions. Eventually, it could harm reachability and energy-efficiency. We therefore propose a novel data dissemination protocol using motion properties of a mobile sink group: slowly varying and streamlike movement. By the slowly varying constraint, the protocol predictively and effectively delivers data to a group through a band of sensor nodes located in front of the streamlike trajectory of the group.