Get a martial arts background. First and foremost, Jackie Chan is a practitioner of traditional martial arts, such as kung fu. His martial arts background allowed him to develop the kind of physical improvisation abilities that characterize his stunt work. So, to do stunts like Jackie Chan, practice a partial art that places emphasis on improvisation.
Dangle, fall and jump from something. While Jackie Chan fills his movie with numerous stunts that involve fighting and improvising with weapons, almost all of his famous stunts have him in the air. In his film "Who Am I?" Chan slides down the side of a building. Similarly, in movie's like "Police Story" and "Project A," Chan dangles from clock towers and stands on top of double-decker buses.
Develop a team. While Jackie Chan admits that he might be crazy, he also makes it known that he's not stupid. To this end, Chan has developed a highly professional stunt team called the Jackie Chan Stunt Team that carefully choreographs, tests and performs all the stunts in Chan's movies. If you want to do stunts like Jackie Chan start working with skilled experts who can supplement your skills.
Use what's around you. One of the most striking aspects of Jackie Chan's stunts is that the actor uses whatever happens to naturally be in the scene. Unlike other movie stunts that set up out of place elements to achieve the stunt, Chan relies on his environment to provide him weapons to fight with, staircases to do flips off of or chandeliers to swing from. So, make the most of your environment to do stunts like Jackie Chan.