Firstly, we know that the mechanism exists for this to be achieved: dogs can already do this and can distinguish which and where human scents have been left.
In the case with Feynman he is claiming a similar mechanism, getting people to touch books that haven't been touched in a while so there is no residual scent and being able to find which book has been touched by comparing a person's scent to a scent left on a particular book. He has a slightly easier job to a dog that is picking up the scent of a stranger running through the bush.
I also have other anecdotes on the net where people have claimed Richard continued to do this as a party trick to non-believers, so it appears it was not a one-off which he refused to do again.
Years later, when Feynman was first at Caltech, he went to a party at
Professor Bacher's house. He was talking to a group of people from
Caltech when the story of smelling the bottles came up. Nobody
believed a word of it. So, Feynman decided to perform the experiment
again. He left the room and had three people touch three different
books to see if he could identify who touched which book. He came
back, smelled everyone's hands, and then smelled the books. He found
the three books correctly and got one person wrong. Yet, the people
still did not believe him.
There is this research paper (extract only) which indicates smells can be picked up between humans, but there results were only better in chance between relatives:
The basis of olfactory signatures mediating human kin recognition was
investigated in two experiments. The odors of mothers and offspring
were correctly matched (by subjects unfamiliar with the stimulus
individuals) at a greater than chance frequency. In contrast, subjects
were not able reliably to match the odors of husbands and wives. These
data support the hypotheses that characteristic individuals odors are
genetically mediated and that kin recognition should be facilitated by
the similarity of such familiar odors among close relatives.
The only other evidence I could find of it being possible is this passage from Darwin's "Descent of Man and Selection in Relation to Sex":
“(36. The account given by Humboldt of the power of smell possessed by
the natives of South America is well known, and has been confirmed by
others. M. Houzeau ('Etudes sur les Facultes Mentales,' etc., tom. i.
1872, p. 91) asserts that he repeatedly made experiments, and proved
that Negroes and Indians could recognise persons in the dark by their
Note this article seems to go into Olfactory Perception in excrutiating detail, if you want go through it in fine detail I suggest this would be the place to do it.