Definitely need some sort of flexible conduit if you want this to last any amount of time, can't beleive it is even legal to install on a tree but I guess it is.
The worst choice would be something like RGC, there is just no give in it. How about a combination of schedule 80 pvc with expansion couplings and sealtight ?
Visiting Disney world, I saw a lot of this type of installation on trees for attractions. ( thats right...I was looking at electrical as I'm standing in line..does'nt everybody ?) They used UF cable though, must have some permission from AHJ I would guess
