How to get system images programmatically? (example: disclosure chevron)

If you mean you can to set the button to use the system disclosure icon, just do as @middaparka suggested and use this:

UIButton *button = [UIButton buttonWithType:UIButtonTypeDetailDisclosure];

If you're asking how you can access the image directly, you can't do that. This is your only option: Use default apple icons for pdfs and docs in iOS app?

From iOS 13 and Xcode 11 you can get system images by giving system name.

let image = UIImage(systemName: "info.circle")

Reference : UIImage Apple Documentation