The two "golden rules" are very similar, but Kant's is strictly deontic and nonconsequentialist. It may even be arguable that its deontic, theological perspective could mandate actions that are not necessarily "good" for a given society or even for "humanity" per se. It is notoriously ill-suited to a complex division of labor in civil society and hence criticized as an empty formalism by Hegel and others.
Rawls is not a consequentialist and is explicitly an opponent of utilitarianism. Nonetheless, his rules do seem more practical than idealist, with hints of a redescription of "state of nature" arguments. Nor are his rules commands to the "will" or eternal souls of individuals, even if no one is watching, so to speak.
To address the question more closely, Rawls derives the "difference principle" from the first two, I believe, and I am wondering if this principle is compatible with Kant's CI? Not obviously. And again, Rawls is generally addressing diverse behaviors where Kant addresses the "will."
The approaches all seem to be in the same spirit, along with Habbermas's "ideal speech situation," and are admirable alternatives to the flaws of utilitarianism. But "derivable"? I can't see them nested in that way. It seems to me hard to get anything from formal CI alone that is applicable to human practices here on planet earth.