"Rage" and "out of control" are so often used with one another that together they stand as a cliche. "The wildfire raged out of control across the state this weekend."
Here, they are being used humorously to exaggerate the condition of the "in-tray." I'm assuming you already know that an "in-tray" is literally a container, most often shallow and rectangular, used to receive "incoming" work; a secretary, for example, might have an in-tray on his desk into which his boss places letters to be answered, bills to be paid, etc. Depending on what you're reading (and I'm betting it's a self-help article or book) the "in-tray" can almost stand as a metaphor for the list of tasks that other people are putting on you.
Anyway, an in-tray raging out of control is simply one that is ungovernable, one filled with a mountain of paper that you can never hope to conquer. Surely you know the sensation :)