Assuming your home page reading settings are configured to display your latest posts in a paginated archive rather than a static page, you can use this PHP code in your child themes functions file to display your sticky posts on only.
If there’s no sticky posts, the default loop of posts are displayed.
To modify the loop on other archive page types, change the is_home conditional tag in the above code.
If your front page uses a front-page.php template with widget areas, you can use the Genesis Featured Posts widget settings to display only sticky posts.