Vision-Language-Action (VLA) models offer a promising end-to-end paradigm for unmanned aerial vehicles (UAVs) to accomplish complex tasks specified by fine-grained instructions. However, standard supervised fine-tuning (SFT) suffers from data scarcity, limited generalization, and weak supervision for nuanced and complicated human intents. Reinforcement fine-tuning offers a natural way to mitigate these challenges and align policy behaviors with human intents through designable feedback, but applying it to aerial navigation remains challenging due to inefficient exploration in expansive continuous spaces. To address these challenges, we introduce an efficient reinforcement learning (RL) framework for VLA-based aerial navigation. At its core, we propose EG-GRPO (Expert-Guided Group Relative Policy Optimization) to augment online rollouts with few-shot expert data. Additionally, we design a heterogeneous pipeline enabling parallel simulation and inference, which reduces rollout time by 43.5%. Across multiple tasks specified by complex human intents, EG-GRPO improves the success rate to 2.13x that of the SFT baseline, while improving intent alignment performance by 60.9%. These results demonstrate that our framework can move aerial navigation toward precise intent-aligned flight.