I do the same as jim. You can buy some tiny brushes in the dental section of any store in the same place you buy dental floss and they work to clean some parts of the brush. I rinse with hot water between every color and run hot water through it before I quit. I also carefully remove the needle and clean between colors as needed and after each use. The tiny nozzle tip I clean again with water and one of those tiny brushes I mentioned above. I don't use any kind of cleaner on it other than water and have painted hundreds of lures with this brush. The key is to never let it get dirty. I do all this over the kitchen sink so be careful you don't drop the tiny nozzle or any other parts down the drain! I put a towel over the drain to prevent this from happening.
This is important, learn what your airbrush sounds like. When it's working correctly it will be a shhhhhhhhhhhhhhhhh sound....when it has some kind of clog it will sound like shkkkkkkkkkkkk.....it's just slightly different but it sounds "scratchy"........if this happens, pour out the paint, run hot water through it and listen to the brush. Look down into the paint hopper. Is there paint stuck on the needle? Does it sound ok? If not, pull the needle out, clean it off, put it back, try again. If it still sounds wrong, the problem is in the tiny nozzle.
Be very careful re-inserting the needle, dont' force it!! If it won't go, wiggle the trigger gently and keep pushing. Go easy. If you bend that tiny tip on the needle you will be buying another one.
RM