I got a couple of jars of jewelery cleaner at the 99¢ store - short, widemouth jar with a basket inside. The jewelery cleaner has some ammonia & detergent in it & works well to soak nipples & small parts. Eventually when the cleaner is too dirty to use (lasts a long time), I just dump it out & refill with water & dish detergent and a few drops of ammonia. Too much ammonia can ruin blued finishes. There's also some tiny brushes used for cleaning under dental bridgework - looks like a tiny tapered nylon bore brush. They work great for cleaning the inside of the nipple & thru the flash hole.
Before reinstalling the nipples, coat the threads with grease of any kind. It doesn't even have to be an antiseize compound. I usually use just a beeswax/tallow ball lube, or even Frog Lube.