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I am always going back and forth between my machines and my barn to see how many of something I have. Animal feeds too. I always run my feed mills and try to keep an even number in stock of each kind of feed. I always have to go check each type of animal to see how many I have left of each type.
I'm pretty sure you can see the number of an item in the barn by touching the item (as if to put it in the machine) and it'll show a small icon with the number in your barn in the upper right corner of the picture. I've been using this for a while and it's quite handy.
Just be careful not to let your finger go in the wrong place and accidentally put an item into production you were just checking the number of. ;)