Khalk is the letter K
There is rune poem for Khalk. It is a Northumbrian rune.
Khalk, the Cup of Dreams, Desires, Hopes, and attainment is reversed today, spilling out what you sought and leaving you unfulfilled and longing. That this rune appears in contrast to the rune of the week, suggests to me that the desires of today are either not going to happen, or leave you feeling unsatisfied. Perhaps the dreams and desires you have need to be re-checked and examined to make sure that what you desire is achievable or really what you desire.
Khalk as an image reminds me of another pair of images found in Astrological Geomancy. These images are Albus and Rubeus (latin for White and Red) and their image suggests of a cup. In Albus, the cup the upright, and indicates peace, accord and dreams. In Rubeus, the cup is reversed, and is conflict (and violence sometimes), intense passions, and dark (and often secretive) desires. I find that those to be an interesting indication as to potential meanings of Khalk as well, with khalk reversed showing that things are conflicted, and the desires involved are unfulfilled because of their dark and secret things, that you may fear to act upon, or only act upon when you can achieve them without notice. I am also reminded that Rubeus also has connotations of sexual acts, that are licentious or perhaps kept secret, which also can translate to Khalk reversed as well.