Human-multi-robot shared control leverages human decision-making and robotic autonomy to enhance human-robot collaboration. While widely studied, existing systems often adopt a leader-follower model, limiting robot autonomy to some extent. Besides, a human is required to directly participate in the motion control of robots through teleoperation, which significantly burdens the operator. To alleviate these two issues, we propose a layered shared control computing framework using human-influenced guiding vector fields (HI-GVF) for human-robot collaboration. HI-GVF guides the multi-robot system along a desired path specified by the human. Then, an intention field is designed to merge the human and robot intentions, accelerating the propagation of the human intention within the multi-robot system. Moreover, we give the stability analysis of the proposed model and use collision avoidance based on safety barrier certificates to fine-tune the velocity. Eventually, considering the firefighting task as an example scenario, we conduct simulations and experiments using multiple human-robot interfaces (brain-computer interface, myoelectric wristband, eye-tracking), and the results demonstrate that our proposed approach boosts the effectiveness and performance of the task.