Staining is done to observe the specimen under the microscope.
Glycerine is a dehydrating agent. It avoids the drying of the specimen. If staining is done after adding glycerine then the specimen will not be stained properly as the stain will be washed off with glycerine.
That's why staining is done before adding glycerine so that the specimen can absorb the stain and any excess stain is removed by adding glycerine.