When developing an MVC application with Kentico, you should always have web farms enabled: https://docs.kentico.com/k12/configuring-kentico/setting-up-web-farms. Web farms ensure that several things are kept "synchronized" between the two environments, mainly cache and physical files (media, attachments, etc).
With web farms configured properly, when you upload a media file to the Kentico project it will automatically be added to the MVC project as well. You can then use our API to generate links to the media file: https://docs.kentico.com/k12/developing-websites/retrieving-content-in-mvc-applications/displaying-content-from-media-libraries.
If you are using page attachments, these are generally stored in the database so you don't need to worry about transferring the files- just use our API to display them. If you store attachments on the disk, web farms will still synchronize them.