Hello! We are glad to hear that you have made use of the RStudio QuickStart!
Unfortunately, the QuickStart is designed to be a standalone demo server for exploring and learning in a private fashion (i.e. just your computer) and is not integrated into actual email servers for email delivery or networking for sharing. As a result, the best way to use the RStudio QuickStart is probably to show your boss in person or via screen-share. There is even a "fake" email account in the QuickStart at http://localhost:5000/webmail/ to see how email works with RStudio Connect.
If you want to take the next step in showing and demonstrating the value of RStudio Connect, I would recommend speaking with your boss or IT team about setting up an actual evaluation of the product, installed on a standalone linux server and integrated with your company's SMTP server. This allows using Connect as it was actually designed to be used, sending emails and such as you describe.
That said, you are correct that the scheduling and customized email features of RStudio Connect are disabled for Shiny applications (that includes RMarkdown reports with a Shiny runtime). Still, if RStudio Connect were installed on a server in your company, then your boss could navigate to a link in his browser and explore the document on his computer. For example, something like:
https://colorado.rstudio.com/rsc/access-to-care/dashboard/
(Which has source code here)
Then there are many ways you could share a link to his email, as @makrez describes. There are many other examples that you or he can explore at solutions.rstudio.com, as well.
In short, I would recommend using the QuickStart to prove the value of RStudio Connect in a limited fashion on your desktop (i.e. sharing support is limited). When that has been done, the next step is to install and integrate RStudio Connect into your company's IT infrastructure. This can be done for free using the 45 day evaluation available here:
https://www.rstudio.com/products/connect/
We are also happy to help navigate the process if you have any questions along the way!