RMarkdown may well be the right tool to use to generate your HTML reports. It's ideal as a template for generating fresh reports when new data comes in.
Your question however seems to be more about the design of the user interface for a website where users can download (or even generate) their reports. This I think is more of a general web design question, it's not really about R. You might even be able to solve your problem by providing a shared folders for each user via a service like Dropbox.
RMarkdown can be programmed to export its knitted output to a particular folder depending on variables such as user ID, or anything else.