The hard part is not to have the handstick collide with the devilstick. So try to toss the handsticks a little higher or to the outside. Also, ther are two ways I have seen this done.
The first is to do the flip as you are lifting the devisltick to toss it to the other hand. The flip is a natural motion while doing the toss. This is the way that I do it.
The second variation is to do the flip after you toss the devisltick to the opposite side. The flip is done about the same time the opposite hand is catching the devisltick. The flip needs to be done much quicker in this fashion since there is not much time before the devilstick is tossed back. The flip looks a little more deliberate this way, but more smooth flowing the previous way.
Walter Park showed me a variation of doing a handstick flip while doing the helicopter. Its about the same difficulty as doing it during an idle.