Answer
Now, spiritually speaking, it is not required to read Chanakya Niti for spiritual understanding or for Krishna consciousness. In fact, spiritual advancement does not depend on reading Chanakya Niti or any similar material book.
However, materially there is certainly some wisdom in Chanakya Niti concerning ordinary day-to-day life and practical common sense. It contains many moral instructions, practical guidelines, and sensible principles which, if followed, can help a person avoid many common mistakes in worldly life.
So materially it may be useful, but spiritually there is no necessity for it in developing Krishna consciousness or attaining spiritual realization.