I also have 2 goats and they range my yard right along with the chickens, chicks, and now ducklings.
I've had no problems thus far. The only problem I had to rectify was the goats getting into the coop and eating the chickens food!
Not to mention, one of my goats (Hershey) thinks she's a hen because I would find her curled up asleep in the nestboxes!
The farmers I got my goats from also keep their goats with their free ranging chickens, geese, ducks, a llama, and sheep. Their only real suggestions to me were to do my best to keep the feeds seperate, and try to give them each their 'own' time to avoid them becoming tired of each other. So I alternate days on who gets let in the yard first and give whichever is out a good hour or more of their 'own' time before letting the others out. Its worked very well for me.
Our local farm vet in town also has goats and chickens, though they aren't free range, but they share a pen AND the coop! And thats the VET!
Cant be all that bad if the VET does it!
As far as getting sick from chicken poo, that would rarely happen because #1) the only way they could get something from your chickens is if your chickens have something and #2) they would have to EAT the poo to get sick, and dispite common rumors about goats, they are quite picky about what they eat, and I doubt I'd ever see a goat munchin away on chicken poo! Oh, speaking of that.....the chicken poo cant be all that bad (if your chickens are not sick of course) because I use an all Organic lawn feed and weed destroyer called Cockadoodle-DOO make from, what else, chicken poo! And my goats eat my grass right after I spray it in, so....
