KC theorem says that, if you have a set of noncommuting observables, then at most one of them can be genuine (i.e., not fake).
First, I don't see how decoherence explain the Born rule, and I would be very happy if you could explain it to me or give a reference where it is explained.
Second, BM can explain the Born rule for positions, without postulating it and without using decoherence. See e.g.
and Ref.  therein.
Third, BM can explain the Born rule for other observables by combining the Born rule for positions with the theory of decoherence.