Flaky tests in web applications frequently arise from nondeterministic interactions between asynchronous events and dynamic DOM updates. Traditional debugging techniques, including fault localization, struggle to diagnose such failures due to the complex, event-driven, and continuously evolving nature of modern web interfaces. This paper introduces DoeFL, a novel approach that combines structured analysis of DOM event sequences with large language model (LLM) reasoning to identify the root causes of web flakiness. DoeFL models temporal causal relationships between DOM events and flaky test failures using Lamport logical clocks. It then uses LLMs to capture semantic inconsistencies and intent mismatches often missed by purely structural analyses. We evaluate DoeFL on 122 real-world flaky test cases collected from 47 web projects. Using only its Lamport-based structural component, DoeFL achieves 47.5% Top-1 and 82.0% Top-5 localization accuracy. When augmented with LLM-based reasoning, performance further improves, achieving Top-1 accuracy between 65.6% and 77.9% and Top-5 accuracy between 89.3% and 95.1%,= depending on the selected LLM.