You generally cannot check in on the app at all, since a DH leg check in requires "extra" input (i.e., your PPR & rotation numbers).

If you check in on delta.com, you can choose to add yourself to the upgrade list(s) (remember, there're two separate lists now, one for FC & one for C+). It's not necessarily obvious or intuitive, but on the first page after you've input your info (i.e., your first opportunity to click "Check In"), there are some boxes you can check to "Request Upgrade." They keep moving around as the site changes, but last I looked, they were over on the far left of the page....