In other words, what is the mind that's having both of these experiences and then attempting to distinguish between them?

When a subject is having a phenomenal experience, certain phenomenal properties are instantiated. In saying that two experiences are phenomenally indistinguishable, I simply meant that they instantiate the same phenomenal properties. As should be obvious, there need not be any mind having both experiences in order for them to be indistinguishable from one another. For example, two people looking at the same patch of red may have phenomenally indistinguishable visual experiences--experiences that instantiate the same property of phenomenal redness. I'm simply asking Jeff to imagine a chicken having a painful experience that instantiates the property of unpleasantness to the same degree that a human child does, when we believe that the child's painful experience is a morally bad thing.

Thomas Nagel famously pointed out that we can't know "what it's like" to be — in his example — a bat; even if we found our mind suddenly transplanted into the body of a bat, all we'd know is what's it's like for us to be a bat, not what it's like for the bat to be a bat.

Sorry, but this is not an accurate characterization of Nagel's argument.