Would the buoyant force increase if I inflated a balloon that's inside
a closed chamber hypothetically submerged underwater? And vise versa
would the chamber's buoyancy decrease if deflated?
First, I am assuming (from the diagram) that the two chambers are fastened to the bottom of the tank and that the chamber walls are rigid.
The upward buoyant force on the chamber should neither increase nor decrease. The buoyant force on each chamber depends only on the weight of the volume of water that the chamber displaces, regardless of what is inside the chamber.
However, the net vertical force acting on the chamber equals the downward weight of the contents of the chamber plus the weight of the water above the chamber acting downward, minus the upward buoyant force acting on the chamber. To the extent that you are adding the weight of air into the balloon on the left, it will every so slightly decrease the net upward force (or increase the net downward force) acting on the chamber on the left compared to the chamber on the right. But the upward buoyant force itself should remain unchanged.
You're correct as the chamber walls are rigid and they're fastened to
the bottom of the tank. Although I forgot to mention the size of them
which is important. Also to make this simple lets say they virtually
weigh nothing & are 1 cubic foot in size 1'x1x'1'. If the chamber was
completely filled with air (in this diagram would be a full balloon in
the chamber) the buoyant force would be around 62 lb or 7.5 gallons.
Does the buoyancy remain unchanged if the balloon was completely
deflated? Seems like the deflation is basically air being vacuumed
from its chamber making it less pressure.
It doesn't matter what the chambers and their contents weigh. Only the volume of the chamber counts. If that volume is 1 cubic foot, the weight of the water the volume displaces is about 62.4 pounds. So the upward buoyant force acting on both chambers would be 62.4 lbf.
Bottom line: The weight of the chamber and its contents only affect the net vertical force on the chamber, not the buoyant force. The buoyant force only depends on the volume of the chamber.
Hope this helps.