This is still an issue on Ubuntu 19.10, using kstars 3.3.6, and as this is the top result when searching for this issue I thought I should reply with my results.
Installing oxygen-icon-theme did not fix the issue for me, but breeze-icon-theme did. This should probably be set as a dependency for the kstars package. I have no idea if this is the right place to point this out or if that should be done somewhere else.
Thanks for all the hard work guys.