Use of motion graphics for other parts of the video

You can save a Project file as a template, then just load it and add the new footage. You can import an AEP file that contains your original animation and then modify the comp without affecting the original project. You can create and save animation presets. You can use the Extended Graphics Panel to organize complex projects and reuse part or all of the comp/nested comp combination to work on new footage layers. 

Your question is a little vague. We need project details and design goals to point you to the most efficient workflow. Screenshots of the Flowchart if the comp has a bunch of nested comps (pre-comps), and we need screenshots of the modified properties of the layer or layers that are used to create the graphic so we understand how you are building the animation. Take the screenshots, drag them, copy and paste them, or use the toolbar to add them to your post instead of using the "Drag and drop here..." button so we don't have to download them to see what is going on. There are just too many different ways to create animated graphics to have any idea of how to help you without seeing your project and understanding the workflow. 

If you are applying the graphic to multiple video clips, the best option may be to create a MOGRT, import that to Premiere Pro, and add the graphic there. You can get very fancy with that kind of work, and it's a lot easier to edit a movie in Premiere Pro than it is in AE because After Effects is not and never will be a video editing app.