“a kind of thing” is not an object. It’s a whole class of objects. So you can’t write “if player carries dollar bill.” The player never carries a class of objects.
I’ll leave it to more experienced Inform users to tell you what syntax to use – my Inform is very rusty.
I think that is my exact problem: after creating a “kind of thing” I’m not sure how how to refer to a specific object of that class. (Particularly the one being carried by the player, or, if both are, then either one, I suppose…)
If the objects of the kind are all identical, you can use “a random kindname” (possibly with some restrictions, such as “a random dollar bill carried by the player”) which is a little counterintuitive if you happen to know that there’s only one, but you can be assured that in that case you know exactly which one the random choice picks.