If the frames are being designed on a computer, CAD tools may help but these are high tech. Companies spend a lot of money on doing detailed analysis for durability and strength of frames. I don't know what design tools people did other than force diagrams and other mechanical engineering things before computers (which use a lot of finite element methods) in the bicycle industry, but a simple civil engineering stress visualization method was building models out of a photoelastic material and seeing where the stresses built up.
Several articles have been written on doing (multiple links) tests for bicycles, normally with some applied stress then measuring deflection. You can try to mimic them on a unicycle to some extent, but they don't have all the same parts that a bicycle has, and testing for trick ability is even harder. They can also build a few frames and run them until they break in stress testing (which would be hard to do if people are building these bamboo unicycles by hand).
Unfortunately, the low tech way to test this will likely be just taking the thing out for a spin (and likely getting injured [especially if the people making these frames don't have experience designing unicycle frames and/or don't understand the properties of bamboo (for example, how do you join 2 bamboo pieces appropriately?)]). There are companies which make bicycles out of bamboo, so you may want to look up some bamboo bicycle builders and try to talk to them about it (since they're botique manufacturers, they will likely not have as much if any testing going on; however, they've likely trained as regular frame builders before so have some intuition on how to design the bikes).
I should add that there are likely legal liability issues which will come up in this challenge - everything stated in this post is at your own risk, obviously. I'd think its non-trivial to make half decent unicycle without having the ability to do tricks to begin with, though.