This is my nicest handstick flourish. It's similar to what some people do with pens and pencils.
Hold the handstick between thumb and index finger, horizontally and almost parallel with your arm but pointed slightly inside. Push the handstick aroung your thumb with your middle finger. In your right hand, this would push the handstick counterclockwise. Let the handstick roll over the back of your thumb a half turn. When done smoothly and horizontally, the handstick will then roll down the inside of your thumb, around the webbing, and up your index finger, returning it perfectly to a useful grip.
Twisting your hand in just a bit at the end will let you continue the stick's spin and seamlessly go from one roll into the next as many times as you like.
The roll can also be done with the handstick vertical. In this case it won't roll around on the webbing to your index finger, so the return isn't quite as smooth and doing continuous spins would be tough this way, but the basic roll may be a bit easier.
Note that this is not the same as the thumb roll flourish described at devilstick.org.