This AddOn shows an image and plays a sound when you get a killing blow. When in a battleground, only killing blows on players are recorded; but all killing blows are recorded outside of battlegrounds.
You can configure the AddOn by editing the options at the top of core.lua in a text editor. This lets you enable/disable the printing of your current KB total to the chat frame and choose whether the AddOn works everywhere or only in BGs.
The KB total is reset whenever you go through a loading screen (e.g. when you enter/leave a battleground).
You can download the AddOn from CurseForge and WoW Interface.
You can view the AddOn's source code on GitHub.
Thanks OligoFriends for the original concept and the art/sound design.
Thanks to nightcracker for ncKillingBlow, which showed me which event fires for killing blows.