Sorry I didn't see this sooner.
Well, truthfully, it sounds like you just saw her eating the way all goldfish do. Especially with a chunk of something. What they do is suck it into their mouths and hold it in the back of their throats. They move their gill flaps in and out becasue there are teeth-like growths on the inside of their gill arches. This enables them to work chunks of things down into smaller bits so that they can swallow them easier. Their lips moving in and out and the rapid gill movements are simply normal chewing movements.
For instance, I have a goldfish that REEEAAAALLLY loves mealworms, especially live ones. Hes a big boy so he can appreciate their size (and yucky juiciness). Anyway, when I feed them to him, he runs around and picks up as much as he can hold in his mouth and sits on the bottom to chew away at them one by one. Sometimes he even gets into it and thrashes his head back and forth like a shark. It's really funny because he has several hanging out of his mouth at one time.
It sounds like all is well though. Good luck with her.