I am creating a new OS X app using Swift and would like to model my toolbar after that delivered in the Mail app. Is it possible to acquire the same image icons that are in the Mail app for use in my custom OS X app?
It may, or may not, be possible to get those icons (perhaps by looking through the package of the mail application). However, if you did use those icons then you could be subjected to legal action for copyright violation. Apple created those images and they are protected intellectual property.
There are several good icon libraries available on the web. Gyphish comes to mind. You might be better served by finding one of those instead of trying to take someone else's icons.