My understanding is that it's always kh at the end of a word. Anywhere else in the word it can be either.
If you ever see it written with a dot in the middle, then it's k, but duolingo doesn't use the dots.
I don't think it's ever pronounced "v". I think the only letters that make the "v" sound are ב and ו.
And I believe the ך (final כ) is always "ch", but כ anywhere else in a word can be either "ch" or "k" (unless it has a dot, then it's "k").