Dynamic flexible assembly flow shop scheduling with multi-product delivery is a critical combinatorial problem, characterized by kitting supply and machine flexibility. Genetic programming is widely used to automatically generate dispatching rules, enabling responsive scheduling that reduces manual effort while meeting high responsiveness demands. However, these methods are dependent on fixed terminal sets and have weak interpretability. In this article, 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 algorithm design and scheduling knowledge. Firstly, multi-stage assembly supply decisions are modeled as priority sorting of directed edges based on heterogeneous graphs. A dual-expert co-evolution mechanism is implemented, where LLM-A generates code while LLM-S conducts scheduling analysis and reflection. Guided by improvements in hybrid evaluation, adaptive rules that fit dynamic features are continuously evolved. Experimental results show that the EvoDR achieves lower average tardiness than state-of-the-art approaches. In 24 scenarios with different resource configurations and disturbance levels totaling 480 instances, it consistently outperforms expert-designed competitors, demonstrating superior robustness.