The only flat item I can think of is a heavy foil baking pan. Durability is always the question mark with these.

A different approach might be the classic Sierra cup. These are light, durable, and extremely useful.

The 10-ounce version is 1-1/2" deep. I find it slips neatly into a cargo pants pocket or even the back pocket of my jeans without being overly annoying.

The 16-ounce version is deeper, but IMO would still be okay in a cargo pocket. I sometimes slip one under my belt during impromptu explorations and don't even notice it's there.