The increasing deployment of Unmanned Aerial Vehicles (UAVs) for military, commercial, and logistics applications has raised significant concerns regarding flight path privacy. Conventional UAV communication systems often expose flight path data to third parties, making them vulnerable to tracking, surveillance, and location inference attacks. Existing encryption techniques provide security but fail to ensure complete privacy, as adversaries can still infer movement patterns through metadata analysis. To address these challenges, we propose a zk-SNARK(Zero-Knowledge Succinct Non-Interactive Argument of Knowledge)-based privacy-preserving flight path authentication and verification framework. Our approach ensures that a UAV can prove its authorisation, validate its flight path with a control centre, and comply with regulatory constraints without revealing any sensitive trajectory information. By leveraging zk-SNARKs, the UAV can generate cryptographic proofs that verify compliance with predefined flight policies while keeping the exact path and location undisclosed. This method mitigates risks associated with real-time tracking, identity exposure, and unauthorised interception, thereby enhancing UAV operational security in adversarial environments. Our proposed solution balances privacy, security, and computational efficiency, making it suitable for resource-constrained UAVs in both civilian and military applications.