Step 1: Do It
Note: my holes are about 1/2 inch by 1/4 inch
Put one piece of tape lengthwise over the hole.
Put another piece of tape laterally over the hole (perpendicular to the first piece).
__DO NOT__ loop either piece over and around the edges of flipflop. This will cause problems in the future.
Flip the flipflops over and put a piece of duct tape lengthwise over the hole.
Step 2: Explanation, If You Care
On the bottom side, the excess stickiness of the duct tape around the edges will collect small pebbles and dirt making a tarlike gook. This tape/dirt amalgum is very good at filling in the hole and keeping it filled. Even after most of the tape has been eroded away, this amalgum stays and keeps the hole filled, it seems to be surprisingly resistant to erosion.
If you wrap the duct tape laterally around the flipflop (as I told you not to do), this shifting of the duct tape wil not happen as well and the amalgum will not form well. Also, because the duct tape cannot shift, it will not collect dirt on the sticky parts as easily and it will keep sticking to the back of your foot, which can get very annoying.
The sticking to the back of the foot doesn't really happen with my method (I've tried both).