kk stands for okey-doke or okey-dokey (in The Macquarie Dictionary 3rd ed, both versions are given, and it's a rhyming reduplication of 'okay' meaning: "yes; all right"). It's a short form of acknowledging a communication to you (especially texts). And it's quick! In other words, to ensure the person who sent you a message knows you received it, a quick "kk" back to them let's them know you have received their message and all's well. As The Macquarie Dictionary is Australian, maybe it's an Australianism.
The Macquarie Dictionary, 3rd ed.