Does Kaluza Klein theory allow one to think of the electric field lines of a point charge or a dipole differently. Is there any insight as to the nature of those field lines?
Unless I am misunderstanding what you mean by Kaluza Klein theory, I don't think so. At least not in an obvious way. What is you understanding of KK?
Kaluza Klein modes are additional massive particles that appear in an infinite tower as a result of making some degrees of freedom periodic over a manifold when compactifying a higher dimensional theory. ()
In such a theory your point charges would couple to the KK modes, I guess. If you started with a higher dimensional photon there'd be something like massive photons mediating the charge too. Is that what you were thinking?