I understand the kids are into this whole "social media" thing, which is why I ask. It might catch on.
The easy way to accomplish this would be to just upload every photo I add to the web site's gallery to a gallery on Facebook as well, but that kind of duplication really rubs me the wrong way. Also, then there are two URLs for each gallery, and which one do I link to? The "real" one, or the one where you can tag yourself and your friends? Making bidirectional links between the photos on the two sites might be possible, but it would be a whole lot of work.
The DNA galleries have been around since long before Facebook existed and I fully expect them to outlive it as well, so obviously "post them to Facebook but not the DNA site" is not on the table.