Large-scale deep neural network (DNN) accelerators are poised to facilitate the concurrent processing of diverse DNNs, imposing demanding challenges on the interconnection fabric. These challenges encompass overcoming performance degradation and energy increase associated with system scaling while also necessitating flexibility to support dynamic partitioning and adaptable organization of compute resources. Nevertheless, conventional metallic-based interconnects frequently confront inherent limitations in scalability and flexibility. In this paper, we leverage silicon photonic interconnects and adopt an algorithm-architecture co-design approach to develop MDA, a DNN accelerator meticulously crafted to empower high-performance and energy-efficient concurrent processing of diverse DNNs. Specifically, MDA consists of three novel components: 1) a resource allocation algorithm that assigns compute resources to concurrent DNNs based on their computational demands and priorities; 2) a dataflow selection algorithm that determines off-chip and on-chip dataflows for each DNN, with the objectives of minimizing off-chip and on-chip memory accesses, respectively; 3) a flexible silicon photonic network that can be dynamically segmented into sub-networks, each interconnecting the assigned compute resources of a certain DNN while adapting to the communication patterns dictated by the selected on-chip dataflow. Simulation results show that the proposed MDA accelerator outperforms other state-of-the-art multi-DNN accelerators, including PREMA, AI-MT, Planaria, and HDA. MDA accelerator achieves a speedup of 3.6, accompanied by substantial improvements of 7.3x, 12.7x, and 9.2x in energy efficiency, service-level agreement (SLA) satisfaction rate, and fairness, respectively.