Flux can only be defined for a planar surface.
False
Flux can be defined for non-planar surfaces.
But how can one do that?..
In case of curved surfaces, flux is first defined through infinitesimal area elements which are a part of the surface. (Flux is scalar quantity btw)
As we assume that a very tiny part of a curve can be approximated to a straight line, similarly a very tiny area element on any non-planar surface can be treated as planar. So, we can find the flux through all these planar elements and sum them up to get the total flux through the whole curved surface.(Flux is scalar quantity btw). Now this is what we affectionately call surface integral. But that’s all the love we have for it right now. You will not have to deal with difficult surface integrals in detail.