Most of the time water and a bulb syringe is enough unless things are really dried and caked. In which case flushing what you can and then soaking for a while usually helps more than most other things. If you're in a hurry, an ultrasonic cleaner can speed things up. Sometimes for converters I'll tear a narrow bit of paper towel, twist it up and shove it down in and scrape around.
There are pen flushes that do help the tougher ones, and some recipes for homemade flushes.