This paper marks the beginning of a series of papers dedicated to establishing the theoretical foundations of a novel theory of relativity called the Theory of Time Frames. Due to the extensive nature of the topic, the theoretical basis of time frames will be divided into multiple papers, each addressing a specific aspect. This initial work focuses on developing a deeper understanding of the flow of time, which serves as a fundamental concept for the theory of time frames. Examining time dilation through the prism of the flow of time revealed a unique opportunity to introduce novel concepts: the background time flow, the gravitational time flow, and the kinetic time flow. Moreover, this exploration allowed for the establishment of the unit of time flow. These pivotal investigations laid a robust groundwork for delving deeper into the impact of the flow of time on various physical phenomena, offering a promising direction for further research in this domain.