Lets say that you are going to do a static flip such that the devilstick is going to do a half flip in a counterclockwise fashion. From the static start position the right handstick gives the devilstick a hard enough push to do a half flip back to the static start position. While the right handstick is pushing up on the devilstick, continue the upward motion at the end of the handstick and give the handstick a half flip. Try to get the timing of both the devilstick flip and the handstick flip such that you catch the handstick just as you catch the devilstick.
You can also do a reverse flip of the handstick as well. For this one lets do a static half flip of the devilstick in the clockwise direction. When the left handstick is pushing up on the devilstick for the half flip, the opposite end of the devilstick is wanting to push down on the right handstick. Use this force to start the reverse flip of the right handstick when the devilstick does its flip. Again, try to get the timing such that you catch the right handstick and devilstick at the same time.
Be sure to work on these flips in both hands, both directions.