Revised for 0.15.6
Placing units into the smelting/input slot from a stack other than the first stack of the same items in the furnace inventory will draw units from the 1st stacks in your inventory even though you tapped on the other stack. I expected the furnace would draw units from the stack I clicked/tapped.
Placing units into the fuel slot works fine if you always move from the same stack, but if you try to then move from another stack, the units will be drawn from the first stack (if you tap) or from some other stack if you use tap and hold.
To reproduce this bug, you need at least two stacks of the same item in your inventory. For example, two stacks of spruce tree blocks (64 and 30 lets say). That's a good example because you can test both slots.
Open the furnace and observe which stack is first (lets say it's the complete stack of 64 spruce blocks). First means top left in the furnace inventory. Select the input slot (and tap/click the other stack (30 spruce blocks) to try to move one unit from that stack into the furnace. A unit moves as expected; however it moves from the first stack (complete stack is now 63) stack and not the stack you clicked. This was unexpected.
Remove all items and close and reopen the furnace. Now move a few items to the fuel slot from one stack. Then tap the other stack to move some from it. A unit moves as expected; however, it moves from the first stack moved, not from the one tapped. If you have 3 or more stacks, tap and hold will move units from a third stack (not the original one and usually not the one you just selected).
I expected that the stack I clicked would more one unit to the furnace slot.
Samsung Galaxy S6 (SM-G920W8), Android 5.1.1
Samsung Galaxy S4 Android 5.0.1 MCPE 0.12.3 (tested touch input)
Asus B121 Tablet Win 10 Pro MCPE 0.12.3 (tested both touch and keyboard/mouse input)