The growing demand for intelligent logistics, particularly fine-grained terminal delivery, underscores the need for autonomous UAV (Unmanned Aerial Vehicle)-based delivery systems. However, most existing last-mile delivery studies rely on ground robots, while current UAV-based Vision-Language Navigation (VLN) tasks primarily focus on coarse-grained, long-range goals, making them unsuitable for precise terminal delivery. To bridge this gap, we propose LogisticsVLN, a scalable aerial delivery system built on multimodal large language models (MLLMs) for autonomous terminal delivery. LogisticsVLN integrates lightweight Large Language Models (LLMs) and Visual-Language Models (VLMs) in a modular pipeline for request understanding, floor localization, object detection, and action-decision making. To support research and evaluation in this new setting, we construct the Vision-Language Delivery (VLD) dataset within the CARLA simulator. Experimental results on the VLD dataset showcase the feasibility of the LogisticsVLN system. In addition, we conduct subtask-level evaluations of each module of our system, offering valuable insights for improving the robustness and real-world deployment of foundation model-based vision-language delivery systems.