That Swedish mess kit is just so neat... a bit large, though, for this requirement:



These are the though requirements to meet.

A stainless steel water bottle would fit your measurements. Or a hip flask that you cut down (but those come with the wretched seams, not something you'd really like to use on a regular basis).

I am perpetually searching for a pot/container with the "cut down hip flask" form factor, but so far I've had little success. If I can't keep the thickness at or below 1.5-2 inches it won't fit a pocket anyway, so then I may as well toss in a small pot in a backpack.

Now I know there are lunch boxes of any shapes available, but using those for cocking is a really flimsy option. A flat tray about 1.5-2" high is hard to keep level over a fire or stove in the bush and the large surface gives a lot of evaporation.



This is the easy and fun part... the Swedish Army mess kit shown above is a very good alternative, but there are literally TONS of options for this size. Anything from coffee cans to Trangia stove+wind screen+mess kit combo will more or less fit within those volume/size restrictions.