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Dynamic flexible assembly flow shop scheduling with multi-product delivery, often with kitting supply and machine-level flexibility, can be found in many applications. It is difficult to design rules manually for it. Genetic programming (GP) has been used to automatically generate dispatching rules, enabling responsive scheduling while meeting high responsiveness demands. However, GP methods are dependent on fixed terminal sets and have poor interpretability. In this work, we develop an evolving dispatching rules framework (EvoDR) that leverages the semantic understanding and generation capabilities of large language models to achieve cross-domain integration of rule design and scheduling knowledge. In our proposed framework, multi-stage assembly supply decisions are modeled as priority sorting of directed edges based on heterogeneous graphs. A dual-expert co-evolution mechanism is proposed, which allows LLM-A to generate code and LLM-S conduct scheduling analysis and reflection. Guided by improvements in hybrid evaluation, adaptive rules that fit dynamic features are continuously evolved. Experimental results show that EvoDR can achieve lower average tardiness than other automatically designed state-of-the-art approaches. It also outperforms expert-designed competitors across 480 instances over 24 distinct scenarios with varying resource configurations and disturbance levels, and EvoDR demonstrates robust adaptability across diverse operating conditions.