Thanks to all of you who offered your best explainations as to the uses of khak shir.
I have to say though, that I think the khak-kishk/kahsk/etc. relationship won't work. Khak shir is not a dairy product of any kind. It's a very tiny reddish orange seed. (I should have mentioned this in my original message.) Perhaps it's ground up and added to kashk???
Until we get a Persian chef to offer his/her expert opinion, I think I'll go with the explanation which stated that khak shir is made into a medicinal drink. It sort of smells as thought it could be used that way.