Maybe the right question is should children do them. There are plenty of videos of the Hardy Brothers practicing on a trampoline as kids. It's the same as any other contact sport, injuries occur. The children should definatly be covered by health insurance for this reason. Also, if you are a parent and other peoples kids are injured on your property you could be held liable for civil and possibly criminal charges, check your local laws. Besides all that, let kids be kids and roughhouse, just keep an eye on them.
A lot of moves are not as they appear. Performing moves based on how they look on TV could thus actually be very dangerous, since one would not be doing them correctly.