Flickering horizontal line when I click on Reading List link
It's more of an annoyance (bug) in Safari than an actual problem because it doesn't cause anything to fail.  It's also definitely not something that can be fixed by resetting NVRAM, the SMC or performing First Aid on your disk(s).

What you are seeing is a dialog box that pops up; usually when you are hovering over a link.  I extracted the frame from your YouTube video clip to see what was being shown and it appears to be the link below the one you have selected.



As you have already said, the problem only manifests in Safari.  Your best course of action would be to provide feedback to Apple so that they can address the issue/bug.  Provide them with a link to this question/answer so they get the full picture (no pun intended). 

Bottom line:  It's nothing more than a box with a document title/link in it and it only appears for less than a split second.  Annoying?  Perhaps.  Problematic?  Not so much.