theme with built-in slideshow/carousel function

I don't think that there is any such theme at this time. Here is a recent spreadsheet I created of all the themes currently available. 
https://docs.google.com/spreadsheets/d/15Cmp7jRsA_rpNXYPKsE1fNRGwjlu-m7rlKzIoirRJJI/edit#gid=0

There are modules that provide pretty easy slideshow support, such that I do not think you need slideshow support in your theme. 

I'm working on a new contrib theme (Tatsu) and would consider providing some support for slideshows or carousels, if I can determine exactly what that means in Backdrop land. I created an issue for Tatsu here, please feel free to comment:
https://github.com/backdrop-contrib/tatsu/issues/26

Do you have the time/skills to create a sub-theme or are you looking for something that will work 100% out of the box?

Here is another forum discussion about slideshow/carousel modules:
https://forum.backdropcms.org/forum/slideshow-carousel-recommendations