The complexity and size of recent deep neural network (DNN) models have increased significantly in pursuit of high inference accuracy. Chiplet-based accelerator is considered a viable scaling approach to provide substantial computation capability and on-chip memory for efficient process of such DNN models. However, communication using metallic interconnects in prior chiplet-based accelerators poses a major challenge to system performance, energy efficiency, and scalability. Photonic interconnects can adequately support communication across chiplets due to features such as distance-independent latency, high bandwidth density, and high energy efficiency. Furthermore, the salient ease of broadcast property makes photonic interconnects suitable for DNN inference which often incurs prevalent broadcast communication. In this paper, we propose a scalable chiplet-based DNN accelerator with photonic interconnects. This research introduces (1) a novel photonic network that supports seamless intra- and inter- chiplet broadcast communication, and flexible mapping of diverse convolution layers, and (2) a tailored dataflow that exploits the ease of broadcast property and maximizes parallelism by simultaneously processing computations with shared input data. Simulation results using multiple DNN models show that our proposed design achieves reduction in execution time and energy consumption, as compared to other state-of-the-art chiplet-based DNN accelerators with metallic or photonic interconnects.