hey erica
As someone who has fed goats for 3 or so years now. I have tried to
feed them everything imaginable on this property. The one biggest thing which will turn a goat off is dirty/soiled grass/shrub and obviously
poop.
My suggestion would be to run the goats first as they will be the picky ones who will want it to be all clean. The chickens might make some areas dirty/poopy which will keep goats from eating the browse.
I am not sure what your timeline is for the goats going onto the area. If it was a year or so after the chickens were in the area it might work fine.
The other thing is the chickens can search through the goat poop and pick out bugs and whatnot who are enjoying the goat poop. Good luck getting a goat to pick though chicken poop lol