In the past several years, social media (e.g., Twitter and Facebook) has been experiencing a spectacular rise and popularity, and becoming a ubiquitous discourse for content sharing and social networking. With the widespread of mobile devices and location-based services, social media typically allows users to share whereabouts of daily activities (e.g., check-ins and taking photos), and thus strengthens the roles of social media as a proxy to understand human behaviors and complex social dynamics in geographic spaces. Unlike conventional spatiotemporal data, this new modality of data is dynamic, massive, and typically represented in stream of unstructured media (e.g., texts and photos), which pose fundamental representation, modeling and computational challenges to conventional spatiotemporal analysis and geographic information science. In this paper, we describe a scalable computational framework to harness massive location-based social media data for efficient and systematic spatiotemporal data analysis. Within this framework, the concept of space-time trajectories (or paths) is applied to represent activity profiles of social media users. A hierarchical spatiotemporal data model, namely a spatiotemporal data cube model, is developed based on collections of space-time trajectories to represent the collective dynamics of social media users across aggregation boundaries at multiple spatiotemporal scales. The framework is implemented based upon a public data stream of Twitter feeds posted on the continent of North America. To demonstrate the advantages and performance of this framework, an interactive flow mapping interface (including both single-source and multiple-source flow mapping) is developed to allow real-time, and interactive visual exploration of movement dynamics in massive location-based social media at multiple scales.