How to disable bouncing icons
 

I unchecked the box in KDE Control Center > Appearance and Themes > icons > Advanced > Animate icons and they're still bouncing. Is there another way to do it?

yes, you have unchecked wrong option. Unfortunately this is more time consuming:
Start K Menu -> Settings -> Menu Editor
or
right click on K -> and select Menu Editor
go to each program and uncheck "Enable launch feedback" option

OK, that works. Isn't there a way to disable that for everything at once?

KControl --> Appearance & Themes --> Launch Feedback

Change the busy cursor in the drop down box to No Busy Cursor, passive, or blinking.