Prebooking-based shared autonomous vehicles hold significant potential in offering convenient and reliable travel services. This study proposes a vehicle trip chain planning model for shared autonomous vehicles, incorporating both company-owned and privately shared vehicles under the prebooking service mode. To address travel time uncertainty, a distributionally robust chance-constrained optimisation model is developed, ensuring feasibility and resilience to time changes, while discussing a computationally safe tractable approximation for ambiguous chance constraints. Additionally, a Divide-Combine Method is proposed to improve optimising efficiency for large-scale scenarios. Validation with New York dataset confirms the effectiveness of the proposed trip chain planning model in meeting demands and reducing operating costs. The integration of privately shared vehicles partly substitutes company-owned vehicles, thus easing the economic burden on operators. Additionally, while a more conservative approach may slightly impact revenue expectations, it ensures smoother execution of trip chains amid unpredictable traffic conditions, underscoring model's significance for operations.