There is no easy way to accomplish this.
And I do not think you could get drag and drop functionality. At best you could use a coded solution but the user would still need to select the particular message. Also this would require your form to be Full Trust and installed.
What about the user creates a zip file of all of the files related to a form, and then attaches that. That may get closer to the functionality they are looking for.
It is good for customers to dream big and reach for the stars, but sometimes you have to give them a reality check. :)