The process is a little bit more complicated than just washing...

The process is a little bit more complicated than just washing the sand out.
At every step of slurry going through a hydrocyclone a portion of larger particles gets removed through the bottom and most of the smaller particles go through to the next stage. This is being repeated until the slurry contains mostly particles below 4 microns with only small proportion of larger ones.
These would be both kaolin and silica.
Particle size distribution of kaolin in GW ore means that almost all the kaolin is under 4 micron and only some silica is under 4 micron.

Both have very similar specific density so any separation based on specific density is not going to be effective.

While reasonably straightforward the process still needs pretty good control system to produce consistent product.