I assume that the wear will be mostly from acceleration force as opposed to deceleration force. I assume that flipping them reverses that and lengthens the life of the surfaces that the balls contact.
I'm not sure how much benefit flipping will actually give you and at least in my case when I've had mildly clicking birfs flipping sides made no difference. I'd put them in so that the surfaces with the least wear are engaged during acceleration and hope for the best.
I couldn't find any solid explanation of which surfaces are engaged for a specific direction of rotation. So, I went out in the garage, grabbed a birf, and figured it out myself. The following is my current thought process. Let me know if you see any glaring errors.
To figure out which surfaces will be incurring wear, we have to think about which parts are "driving" which other parts. In this case, the inner axle shaft is imparting force to the star in the birf, which in turn applies force to the ball bearings, who then drive the outer bell and attached shaft, which then drives the drive flange and so on. The relationship is important because it establishes certain points of contact within the assembly. Based on this relationship, I deduce the following area will see increased wear within the birf:
1.) The rear side bearing surfaces of the star
2.) The front side bearing surfaces of the bell
3.) The rear side of the bearing slots in the cage
The words "front" and "rear", as used here, are in reference to the vehicle as a whole with the birfs installed. This is why swapping sides could, theoretically lengthen the life of the joint. They only wear in one direction (unless you do a disproportionate amount of driving in reverse).
Here are pictures of my passenger side birf. You can see here the wear inside the bearing tracks of the bell. As expected, the greater wear is on the left hand side when looking into the bell. The "left" side would also be the front of the vehicle as viewed from the diff in the installed orientation.
This next picture is of the cage. You can see that the larger divots worn by the ball bearings are on the rear sides of the slots. The wear seems to occur on the inboard (closes to diff) edge of the slot.
Finally, this picture shows the wear to the star insert. As explained before, increased wear is seen on the rear sides of the bearing channels. This happens as the star "pushes" the ball bearings into contact with the bell.