How does Buckingham's speech in act 3, scene 7, lines 24-41 support the Scrivener's speech at the beginning of the scene? What other characters in this scene act in ways that bear out the Scrivener's speech?

The Scrivener is an important minor character in Richard III. Formally, the Scrivener's role is to draw up documents. But in relation to the play, his dramatic role is to provide a running commentary on events, in particular drawing attention to the devious machinations of Richard and Buckingham. His speech in act 3, scene 7 is an example of this.
The Scrivener is also presented to us as a man of the people, someone with his finger on the pulse of public opinion. The Scrivener, much like the common folk of England, knows that Richard and Buckingham are up to no good. Yet the latter is largely unaware of this, expressing great surprise at the mute hostility of the crowd in response to his speech. But their reaction is entirely predictable, and is foreshadowed earlier in the scene by the Scrivener when he complains about spending practically a whole day drawing up Hastings's indictment. The whole thing is a sham, and the Scrivener, for one, can see right through it:

Who is so gross
That cannot see this palpable device?
Yet who so bold but says he sees it not?

You'd have to be pretty stupid not to see through this blatant ploy, says the Scrivener, but who would dare to come right out and say this? The behavior of the citizens, the Lord Mayor, and Catesby later on in the scene would certainly appear to bear out the Scrivener's words. They are indeed stupid enough not to see Richard's theatrical rejection of the crown for the gigantic con trick that it is. The common people, like the Scrivener, are on to Richard, but not the worthies of the city. They are completely taken in by Richard's fake reluctance to accept the crown of England and by his loud protestations of loyalty to young King Edward.