The rapid expansion of the low-altitude economy has propelled the increasing cross-domain applications of unmanned aerial vehicles (UAVs). During cross-domain missions, UAVs face challenges in identity management and trajectory privacy protection. The conventional centralized identity management model is susceptible to single-point failures and blockchain-based solutions suffer from performance bottlenecks. Also, the high dynamics of low-altitude networks further exacerbates the risk of trajectory data leakage. To address these problems, this paper proposes a consortium blockchain-based cross-domain authentication and flight trajectory privacy protection scheme, which includes cross-domain authentication, key agreement, dynamic identity changing, mutual authentication and domain notification methods. The proposed blockchain-based method enables trusted cross-domain identity verification, preventing attackers from reconstructing full flight paths with partial information. Formal verification based on the real-or-random model is presented to prove the semantic security of the proposed method. Informal security analysis ensures that the proposed method resists major cyber attacks. The performance of the proposed method is evaluated through simulations. The experimental results show that the proposed method has higher efficiency compared to the existing methods.