Does anyone know or have ideas for a mechanism to make bird wings flap on a rod puppet?   

I wish I had more pictures available, but they are in a computer that is currently dysfunctional. The top picture is the bottom of a pill bottle with slots cut in the sides for the tongue depressors which served as supports for the wing. The bottom picture are the parts for the bird body, wings, tail, tongue depressors and pill bottle. The holes in the depressors are connected with elastic, and then there is another short piece of elastic that is tied around the center point between the wing struts and run through a hole at the top of the bottle and tied off there. That elastic pulls the depressors upward in the pill bottle, putting the wings in a downward position. There is a piece of fishing line tied at the same place going downward, and attached to a trigger on the handle of the rod that supports the bird. That rod is made of spring wire. As the trigger is pulled downward, the line pulls the depressors downward, raising the wings. Releasing the trigger returns the wings to the down position.

Below is a video demo of the prototype.

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https://youtu.be/p_B7Hsosb18

This may not be the most elegant solution to the problem, but I'm definitely not an engineer, and had to use materials I had at hand. I was very pleased that I was able to invent any kind of workable mechanism. It turned out to be sturdy enough to withstand a trip to Siberia and back with multiple performances during the journey.