I'm looking for a chart like this:
Basically something that tells you whether an app with a given license can be linked with a library of a given license.
Does such a thing exist?
It's unlikely such a thing, as described, exists: there are many definitions of what constitutes a FOSS license and even more licenses. Such a graph would never be canonical or authoritative.
However, GNU and the Free Software Foundation (and by extension, Wikipedia) have taken great pains to document which licenses are GPL-compatible (and subsequently "FSF-approved"):