I found a work around for this problem. It seems to be caused by using a custom icon theme that's missing some icons that BasKet uses. I was experiencing exactly the same problem today when I first leaned about basket and decided to give it a trip. However, launching BasKet with a new user account so the default KDE icon theme is used, or switching the icon theme back to the default one in KControl solves the problem for me.
I found a work around for this problem. It seems to be caused by using a custom icon theme that's missing some icons that BasKet uses. I was experiencing exactly the same problem today when I first leaned about basket and decided to give it a trip. However, launching BasKet with a new user account so the default KDE icon theme is used, or switching the icon theme back to the default one in KControl solves the problem for me.