Flux is an application architectural pattern developed by Facebook. It was developed to solve some of the complexities of the MVC pattern when used at scale by favouring a uni-directional approach. It is a pattern and not a technology or framework.
When applications that use the model-view-controller (MVC) pattern at any scale it becomes difficult to maintain consistent data across multiple views. In particular the case whereby flow between models and views is not uni-directional and may require increasing logic to maintain parity between views when model data is updated. Facebook hit this issue several times and in particular with their unseen count (an incremented value of unseen messages which is updated by several UI chat components). It wasn’t until they realised that the MVC pattern accomodated the complexity that they stepped back from the problem and addressed the architecture.
Flux is intentionally unidirectional.