In R, the Royston-Parmar model(s) can be calculated with functions in the flexsurv package. It also includes a qsurvspline function gives a quantile functional. So computing the survival time for a 50% survival should be fairly straightforward.

    ?qsurvspline

However that doesn't seem to take a model argument and apparently only handles the simplest of cases. Looking at the help page for `flexsurv` we see that there is a `summary` function that can derive quantiles,and it does accept your model argument:

    summary(mod, type="quantile", quantiles=0.5)
     
      quantile      est      lcl      ucl
    1      0.5 319.1645 280.6714 364.0389