By adding 'Related Lightning Component' on the record page you can download the files from a related object, to achieve the requirement follow the below steps:

1. Open any of the records that you want to use for downloading parent object files, In the example - Select Account record. 

2. Now click on the Edit Page button.

2. Drag and drop the 'Mass file Download Relate Files' component on the screen and then if you want to see only related objects that have a file then check the 'Show only Object having related files' checkbox and hit Save.

3. Now go back to the record page and check that component, here you can see all related files are showing and in one click you can download all Files/Attachments.