As far as I can tell, there is no way to extract the distance for each case. If I understand correctly what you want, you can encode your own:
sqrt(rowSums(iris[,1:4] - fitted(kmeans_iris)) ^ 2)
#[1] 0.058 0.642 0.742 0.742 0.058 1.258 0.442 0.042 1.242 0.542 ...
... .