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Over recent decades, the tourism industry has demonstrated progressive expansion, driven by advancements in aviation technologies and shifting consumer interests. In this context, online flight itinerary ranking has become a pivotal business for Online Travel Platforms (OTPs), which aim to rank flight itineraries by synthesizing real-time flight data provided by airlines with users' individual travel preferences. Currently, most OTPs rely on rule-based methodologies or rudimentary user preference-driven models to address this task. However, these methods are inherently limited by their insufficient consideration of delayed booking behaviors and their neglect of dynamic contextual attributes associated with flight itineraries, thereby undermining their ability to effectively handle the intricacies of flight ranking. To address these shortcomings, this paper introduces the Delayed Conversion Modeling based Personalized Flight Itinerary Ranking Network (DCRNet), designed to improve ranking accuracy by integrating delayed booking patterns and contextual dependencies into the modeling framework. Specifically, DCRNet explores the dynamic associations between users' current contextual information and their historical travel records, and models users' delayed booking behaviors via a masked attention mechanism. Moreover, an enhanced multi-task learning framework is employed to effectively integrate traditional behavioral modeling with delay-aware modeling, thereby improving the overall prediction accuracy and enhancing the system's personalized recommendation capabilities. Extensive offline experiments conducted on real-world datasets from Amadeus and Fliggy demonstrate the superior performance of DCRNet. Furthermore, its successful deployment on Fliggy's online itinerary search system has yielded significant improvements, underscoring its practical effectiveness and scalability.