There is no shortcode that provides the link to post submission page. If you want to have a menu link, the way I can see it working is like this:
1. Create a new page called let’s say “Submit Post”
2. Add this page to the menu
3. Show this menu link ONLY for logged in users that have the capability to Submit posts
3. If the user goes to the provided menu link, do a redirect to the real “Submit Post” page.
Would this work for you? If yes, of course I can help with.