Can death records be sealed?

As a general rule, the only ones who can get a death certificate are family members. So if a family member gets the death certificate and wants to post it online, then that is something that they can do. If it is a non-family member, the problem is going to be getting a copy of the death certificate but if they get it, there is nothing that stops them from posting it on Facebook. You would need to contact the Tennessee Office of Vital Records about making sure that non-family members do not get it.