In Classic Version, we can directly/programmatically call the MFD tab with records pre-selected. Just create a URL (like below) and add IDs with a semicolon ( ; ) as a separator between records IDs (of the same object records), and it will show files belonging to multiple records specified in the URL 


For eg: You can use the below URL and add the IDs using a semicolon. 


/apex/MassFileDownload?parentid=0015g00000yBINzAAO;0015g00000yBIO1AAO;0015g00000yBINyAAO