If you're using Shopify Payments and qualify for a 1099 you would find a download link on the payments page. Only the account owner will see this link.
Kassey here from the Shopify Guru Team! There could be a couple of reasons why you're not seeing the button in your admin; you would need to be logged into the Shopify admin under the account owner to be able to see the button and you would also need to have made 20K through Shopify Payments alone for 2015. If you've made sure both are covered but still don't see the button, we can start a private thread via email and I can look into it for you. :)