Is there a way to set a rule on the email client for when I receive a certain email with a subject line to have it print out on a printer?
Not a built-in method, no. However, you might use some clever workarounds to do this. For example, most of the new HP wireless inkjet printers have an email address and whatever you send to that address gets printed out. So, you could make a rule to forward emails to that printer’s email address and they would print.