[pkscout]

In order to minimise the size of my Kodi/.kodi folder when I store a backup or, transfer my build from my laptop to my android box, which folders/files am I able to remove from the Artist Slideshow folders without affecting addon/settings?

That kind of depends.  If you're not using any images you downloaded from other sources (manually or using some other addon), then you could probably remove everything except the settings.xml file which is in userdata/script.artistslideshow.  AS will then download images again as needed.  If you have downloaded images from other sources, there probably isn't much of anything you can remove safely.

Please, please, please validate this before excluding a bunch of stuff from your backups though.  I've not done any testing on how much stuff you can remove from AS storage before you notice.  Drives are so cheap I've always used the "backup everything, sort it out later" method.