That's a view of phenomenal experience (namely, that phenomenal properties are intersubjectively comparable, and that "phenomenal properties" can be described from a third-person perspective) that is far, far from uncontroversial among professional philosophers, and I, personally, take it to be almost entirely unsupported (and probably unsupportable).

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.

Intersubjective incomparability of color experiences is one of the classic examples of (alleged) intersubjective incomparability in the literature (cf. the huge piles of writing on the inverted spectrum problem, to which even I have contributed).

... imagine a chicken having a painful experience that instantiates the property of unpleasantness to the same degree that a human child does...

I really don't think this is a coherent thing to imagine. Once again — unpleasantness to whom? "Unpleasant" is not a one-place predicate.

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

If your objection is that Nagel only says that the structure of our minds and sensory organs does not allow us to imagine the what-it's-like-ness of being a bat, and does not mention transplantation and the like, then I grant it; but my extension of it is, imo, consistent with his thesis. The point, in any case, is that it doesn't make sense to speak of one mind having some experience which is generated by another mind (where "mind" is used broadly, in Nagel-esque examples, to include sensory modalities, i.e. sense organs and the brain hardware necessary to process their input; but in our example need not necessarily include input from the external world).