Also, make sure you didn't turn on "receive only from links" in stockpile menu or set "take from kitchen 2" instead of "give to kitchen 2".
I start embark with "gather all" single stockpile for everything, but refuse and corpses stockpiles, with max bins and max barrels. So trust me, this works always, so this is not the issue for sure.
I make sure in orders there is "no-mix" (o->m). Mixed barrels and bins are a nightmare bug to fix and it is still allowed by default by some unimaginable reason. You need to mark them (and hope no fluids inside) with d->b->d and then tediously unmark dump from each and every single barrel and bin, so only insides get removed (alike stripping goblinite from goblins inside cages).
Also I never ever use bins! Horrible things. The red trail of "bin is inaccessible" messages is more then annoying. I would suggest checking on quantum stockpiles on wikipedia and making few light wood minecarts for the needed stops. Then sell bins to merchant and never ever do them again. Hauling route menu is a little an acquired taste in setup, but once you get used to tackling this fiendish gui, then your Dwarf Fortress' life can receive a miracle of automation. That makes this game a lot more fun to play, when you do not need tediously tend to every single micromanagement issue. Even with hauling route clearing off about 50 automated jobs, I still have 30 automated jobs in manager, because brewing 18 alcohols without automating them from fields to stills, would be a game-stopping harassment.