Timely and accurate assessment of damages following natural disasters is essential for effective emergency response and recovery. Recent AI-based frameworks have been developed to analyze large volumes of aerial imagery collected by Unmanned Aerial Vehicles, providing actionable insights rapidly. However, creating and annotating data for training these models is costly and time-consuming, resulting in datasets that are limited in size and diversity. Furthermore, most existing approaches rely on traditional classification-based frameworks with fixed answer spaces, restricting their ability to provide new information without additional data collection or model retraining. Using pre-trained generative models built on in-context learning (ICL) allows for flexible and open-ended answer spaces. However, these models often generate hallucinated outputs or produce generic responses that lack domain-specific relevance. To address these limitations, we propose ThiFAN-VQA, a two-stage reasoning-based framework for visual question answering (VQA) in disaster scenarios. ThiFAN-VQA first generates structured reasoning traces using chain-of-thought (CoT) prompting and ICL to enable interpretable reasoning under limited supervision. A subsequent answer selection module evaluates the generated responses and assigns the most coherent and contextually accurate answer, effectively improve the model performance. By integrating a custom information retrieval system, domain-specific prompting, and reasoning-guided answer selection, ThiFAN-VQA bridges the gap between zero-shot and supervised methods, combining flexibility with consistency. Experiments on FloodNet and RescueNet-VQA, UAV-based datasets from flood- and hurricane-affected regions, demonstrate that ThiFAN-VQA achieves superior accuracy, interpretability, and adaptability for real-world post-disaster damage assessment tasks.