I think that the knowledge would be minimal. Maybe know how to ID a Douglas fir from a redwood.
The climber would not need to know much botanical stuff. All they would need to do is take images at intervals including close-ups. With good photos, the scientists could figure out what the plants were. Doubt they would want samples removed anyway.
It would be nice if the height of the photos could be known, or the estimated height. With a person on the ground, one person could read a tape and radio for each area a photo was taken, but good chance both people would enjoy climbing simultaneously. Unless a non-climbing volunteer went along.
Like, if you took this photo, you would not need to know the ID - just say what tree and and about how high (At tree top, a GPS would probably work well too):

Also, a laminated cheat-sheet could be supplied. There is only a limited number of species that are common. But I'd imagine that such a project would function well, simply by an abundance of images showing how much of what is at various levels.