Leveraging the power of flexible visual presentations has become an effective way to aid information interpretation, decision making and problem solving. It is indispensable to address the high complexities with visualization problems and relieve the impact from the intrinsic limitations of human cognitive capacity. Addressing these problems raises demanding requirements for information presentation flexibility. However, many existing visualization systems tend to provide weak support for such flexibility due to the issue of closely coupled information representation and presentation in system designs. This issue limits their support for rich presentation options, flexible presentation integration and reusability, and vivid storytelling of data. To help with addressing these problems, issues and requirements, this paper generalizes typical presentation models to provide paradigm level support for achieving presentation flexibility, and identifies key requirements for presentation development to accomplish the flexibility at a system level. With articulating the requirements at both paradigm and system levels, the paper proposes a user-centred process to realize presentation flexibility by meeting both functional and cognitive requirements for information presentation. The proposed theory is validated against a real-world business case and applied to guide the development of a prototypical system, which is demonstrated through a sequence of scenario-driven illustrations.