Keyboard shortcut for buttons in dialogue box

There is no set keyboard shortcut for the Delete button in this case. If you have enabled full-keyboard access in System Preferences → Keyboard → Shortcuts, you can use the Tab key to move focus to the Delete button, and press Space or Enter key to invoke the Delete command.

Using the Tab key, you can move the focus to the Delete button.

Almost, though not quite, universal on macOS is the use of Cmd ⌘ Backspace ⌫ [or Delete on keyboards without a distinct Backspace key] to discard, or discard changes.

This should also work to invoke "Don't Save" in dialogs too.
Some apps still accept the alternative of Cmd ⌘ D to do this, but Backspace has been the recommended method for several years [since Lion or so].