chicken necks are pretty small to expect a Brittany to actually chew. I wouldn't be worried, even if she throws it back up and then eats it again. That's just what they do. They can digest the partially chewed chicken necks just fine.
You can try looking for large turkey necks and give those frozen. That would be a more appropriate size for a dog your size if you want some chewing action to help with keeping teeth clean. You should also consider getting large bones just for chewing, like beef knuckles or leg bones. Dogs do need to digest some bones and they do need to chew some to keep those teeth clean, but that isn't always a 2 for 1 deal.