Hi Zigfire
If your chuck is in good condition the scroll will be a very close fit in the body, There is little room for chips to get behind it via the gap around the edge. In fact when disassembling the chuck it is not an easy job to get it out, if it is angled slightly it will stick, requiring gentle taps with a brass drift through the jaw slots to straighten it and enable it to be eased out.
I use compressed air to keep the area between the scroll and the jaw threads clean.
After removing the jaws and using a compressed air nozzle held against the square groves in the scroll and against the corner of the body (At the back of the Jaw slot) and at the same time slowly rotating the scroll with the key you can clean out the grooves. the muck will be blown out the opposite hole.
The scroll will guide your nozzle along cleaning the entire spiral as it turns if the nozzle has an edge that will engage the groove.
If you do this in both directions the chuck will be clean. The jaws themselves can be cleaned in a little spirit.
There is no risk of blowing swarf deeper into the chuck due to the large jaw openings. pressure is not built up.
I only ever lightly oil the scroll so it does not attract dirt.
I had to do a lot of boring recently… a process always inclined to fill the chuck with swarf particularly on larger diameters where the scroll is exposed, and the boring bar passes the inside end of the work. I had to do this cleaning process a couple of times.
Any time when adjusting the chuck and I feel the key resistance increase as the scroll hits an obstacle (swarf) I use this method to clear it. It works
I now only dismantle the chuck very occasionally.
Regards
John