[I assume your question is about repeating the action of adding to the main screen, rather than copying the look of the button itself (which is pedantic is what you actually wrote).]
As others have said, this is not possible.
What you can do is programmatically launch Safari from your application and provide the URL of the download page, which is your page.
When your page is loaded, it has some animation and shows the user where the add button to the main screen is located, and ask him to click it after clicking the link displayed on your web page. When users click on a link, it takes them to any page that you want to save on your desktop, and you hope that they follow your instructions.
If you register your application for processing a proprietary URL scheme, users can return to your application from Safari by clicking on the link using the application URL scheme.
The web pages that you download Safari, however, must be deleted pages, you cannot specify Safari on the page in your application or load the application, because Safari cannot read pages from your application sandbox.
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