Does the persona 4 trophy for all social link completion flag from the items they give you (which carry over to new game+) or from actually hitting rank 10? What I mean is, on a second playthrough, could I only do the links I missed maxing my first playthrough and earn this trophy or do I need to reach rank 10 with all social links in a single playthrough??
According to Playstation trophies, you're supposed to max all S-Links in a single playthrough:
This trophy requires quite a lot of planning and must be done on a single playthrough. You should always remember that you gain more 'social points' by having a Persona of the corresponding arcana in your inventory, I also suggest doing this on your second playthrough as certain answers require certain Social Status, e.g. Max Courage and you should have those maxed by the end of your first playthrough.
The items you get for clearing a particular S-Link allow you to fuse very specific personas that can only be obtained after maxing the S-Link associated to its arcana. They are not meant to be a shortcut for the trophy.