Are you aware of any R library that does the Koppen-Geiger climate classification, once the necessary input gridded (rasters, netcdf etc.) data are provided?
I have not seen anything that allows you to provide the underlying gridded data and then preforms the classification. However, there is the kgc package that identifies the Koeppen-Geiger Climatic that a given [x,y] coordinate pair resides in. You could coerce your raster into a SpatialPixelsDataFrame object and then iterate through the @coordinates slot to find each zone and then assign it to the corresponding row in the data.frame residing in the @data slot. The index would be the same for both slots.