Kinetic energy of a balloon

There are two components to the total energy in the balloon:

1) The P*V work done on the air (or whatever fluid you've filled it with) and

2) the stress*strain work done on the rubber as the balloon expands. The latter is tricky to calculate (due to rubber's nonlinearity, large-strain modeling of the membrane, etc.)

If one starts from an uninflated balloon, all the work is done by forcing the fluid into the balloon. So you might measure the pressure and flow rate (dv/dt) -- ideally sampled simultaneously) -- from uninflated to the bursting point, and numerically integrate P * delta_Volume, from (negligible initial volume) up to the bursting volume (and pressure) of the balloon.

My guess is that consumer balloons have somewhat uneven wall thicknesses, so expect a fairly wide range of results.