The chicken skeleton in the photo is not an easy project. Actually, I found cleaned chicken bones that kids can safely handle more useful and certainly easier to obtain than the full assembled skeleton.
Boiling is one method of cleaning the flesh from bones. It is not the preferred method if quality specimens are needed. This is because boiling can shrink bones.
The negative effects of boiling are negligible compared to how easy and inexpensive this bone cleaning process is.
Instructions for De-Boning A Chicken by boiling are found Here: HOW TO CLEAN THE FLESH FROM CHICKEN BONES