I haven't seen anyone solve this. I think it would be reasonable to do a time point by time point averaging (over multiple imputations) of the underlying survival curve, although there is some question about whether to "freeze" the centering constant (sum of beta times covariate mean). What will be harder to get is confidence intervals for predicted probabilities after multiple imputation. I hope someone will take up the challenge.
Robert Long wrote
I am working with some survival data with missing values.
I am using the mice package to do multiple imputation.