Can't put used chest on donkey or mule

I have tamed a two donkeys, and bred a mule with my horse. I have tried to ride the donkey and mule and put the chest in it's slot; but there is no slot. I have put the chest in my hand and right clicked on the rear leg of them, but it just causes me to ride them. I have held down the shift button and right clicked; it just opens their inventory without equipping the chest and without me riding it. The only animal that I can equip a chest to is a llama, and I only had one at the beginning of my world, but it died. I don't know what else to try or if it is just impossible to equip chests to donkeys or mules at this point. Help would be much appreciated.