Here you can read how to build a rubber band powered airplane with clapping wings.
Step 1: Part 1
The first part is the base part to hold the rubber band in place and to produce a rotational force. You can make it as long as you like, I made it as long as two rubberbands.
Step 2: Part 2
The second part is the mechanism that makes the wings clap.
Step 3: Part 3
How i made my wings: it's a basic wing, with the profile of an airplane wing. I used broad rubberband to attach the wings to the second part to reduce friction. Again you can change the lengt of the wings, if you make the wings too long the rubberband will not be able to make the wings clap.
Step 4: Final Assembly
I added some surfaces to the base so it goes farther and doesn't spin.