On my Evening Star there is a hole drilled through the axle to a cross hole in the axle where it sits in the axle box. Grooves and other holes will let the oil move around.
The book suggest pumping thick oil through the hole which should be easily accessible from the side of the wheel.
To me this would have the effect of flushing the bearings and the axle box.
It just needs a pump with a cone that will go into the small hole.
Clive