Dropp
If you go onto the portal you can find the link for the flight time since day 1 at EK, or any dates you need to put in. For example, a number of airlines want the last 3 pages of your logbook or so, but you'll probably also want to print out the first page as it has your total time in whatever jet you're flying at EK.
Then, go get them stamped and signed by the chief pilot. No issues at all. They're probably used it by now with sheer numbers leaving!