This is how I polished the inside of my airbrush nozzle. I was not satisfied with just thinner in removing dried up paint.
What I used:
1. Mini drill
2. Rolled tissue (if you roll it really fine, it would reach the outside of the nozzle)
3. Tamiya polishing compound
Taped the other end of the tissue to fit the drill chuck. Mounted the drill on a table clamp like so:
Using a toothpick, I applied little amount of polishing compound on the tip of the tissue. Inserted the tissue to the nozzle first using a parts clip before turning on the drill. Never underestimate the power of the turning tissue. It could warp your nozzle. Polish lightly. I couldn't get a decent photo of the inside of the nozzle after polishing, but it was really shiny.
Managed to get a picture of the polished nozzle.
This is a 0.2mm nozzle
This was taken very close to my desk lamp bulb to get a good glimpse of the shine.