I don't think there is any equivalency.... A watt is
W = J/s = (N*m)/s = ((kg*(m/s^2))*m)/s = kg*(m^2))/(s^3)
Therefore: W*kg = (kg^2)*((m^2)/(s^3)) which is not equal to N = kg*(m/s^2)
I guess the closest answer would be :
1 kg*W = (1 kg*m/s) N or
1 kg*W = (1 N*s) N