Hello Richard,
It is little different to cleaning a standard three jaw chuck really. The added features of the individual cones that make the micro adjustments to individual jaw setting take quite a lot of patience to get right afterwards.
Ideally you need a good test bar gripped in the jaws for the work along with a DTI but a reliable piece of silver steel will do instead.Use the hex key on the cross bar of the chuck key to make those adjustments, checking by DTI close to and 2 or 3 inches away from the chuck before nipping up the backplate bolts. Then check again and repeat if things have moved
The chuck should hold those settings for that diameter for a long time afterwards.
Light oil is the correct lubricant
Regards
Brian