I use jetpack carousel for all of my galleries , even for my featured image, my question is, how do I style my [gallery] outcome to use different CSS for the featured image so I can manipulate it a little bit but not mess with the regular default galleries outcome?
What I would do is open it up in chrome, inspect element, and check to see if the featured image has a different ID or CLASS to the other images in the gallery. Then I would add an additional line to my CSS that targets those ID/CLASS.
In the event that a ID/CLASS aren't unique I would be looking into inspecting the plugin, and adding my own declaration (strongest thing in wordpress for me is that a lot of elements have classes/id's)
If you need further detailed help, I'm happy to edit this answer in future just let me know.