Real-world trip planning requires transforming open-ended user requests into executable itineraries under strict spatial, temporal, and budgetary constraints while aligning with user preferences. Existing LLM-based agents struggle with constraint satisfaction, tool coordination, and efficiency, often producing infeasible or costly plans. To address these limitations, we present TriFlow, a progressive multi-agent framework that unifies structured reasoning and language-based flexibility through a three-stage pipeline of retrieval, planning, and governance. By this design, TriFlow progressively narrows the search space, assembles constraint-consistent itineraries via rule-LLM collaboration, and performs bounded iterative refinement to ensure global feasibility and personalisation. Evaluations on TravelPlanner and TripTailor benchmarks demonstrated state-of-the-art results, achieving 91.1% and 97% final pass rates, respectively, with over 10x runtime efficiency improvement compared to current SOTA.