Is there a way to limit / enforce permissions on image style downloads? I have a few image styles that I only want certain node types to be able to view because certain images on my site have an open license for use and so I have a style for a large image gallery view, while others do not and so they shouldn't use this style. 

The images, and the image styles are stored in private locations and served through Drupal. 

Is there a way I can set conditions on when an image style can be downloaded for an image; for example by node type, a field flag, or who a user is logged in as?

Is there another solution to this issue?
This is not really possible. The module the create this doesn't care or know where the image comes from, so you can't make any permission checks like that. It would be possible to display such images through custom theming Views and many other ways which makes a 100% failsafe permission check more or less impossible.

You can make sure nothing like this will happen based on how you setup your site, and you could add some extra security by overwriting the settings/rendering for image fields, but it won't be 100% fail safe.