You asked two questions.
1- "How can this design be improved upon to make it more effective?"
There is no original design. The picture you have shown has nothing to do with piezoelectric energy.
2- "Could a tree harness kinetic energy through the wind blowing long flexible branches?"
Answer is as follows.
Using Mechanical Vibration to generate Electricity.
One way is shown here in which, a lead zirconate titanate wafer is used as tranducer. In it, LED can be replaced with a bridge rectifier and connected to a battery to charge it.
Multilayer polyvinylidene fluoride (PVDF) films can be attached to the vibrating branches of the trees with proper wiring and circuit to charge batteries.
As told here
For functionality test, the highest voltage produced for a single film
PVDF is 0.368 V which charges up a capacitor to 0.219 V in one minute.
The highest voltage produced by multiple PVDF films is 1.238 V by
stacking 10 films of PVDF in parallel which charges up to 0.688 V in
one minute. For application test, 5 pieces of PVDF films were attached
to a glove to generate some voltage during fingers bending activity.
The highest output voltage recorded is 0.184 V which stores 0.101 V in
a capacitor after 200 times of hand bending and releasing.