Learn fine art for cinematography?
If you want to develop your craft beyond just technical proficiency then I'd say that being open to the broadest range of influences is crucial. 


For example: if you want to learn about lighting for portraits or interviews, go look at Rembrandt or Vermeer. You can learn a huge amount from the way the old masters used light and composition.

As for where to start: go to a gallery. Walk around and find an artist that you like, whatever style it is. Read about them and take it from there. A good intro to the history of modern art movements (Impressionism onwards) is the book What Are You Looking At? by Will Gomperz.