The only way you could get lift from a gas sac is if it was a light element like helium or very hot, making it less dense than ordinary air. Both would require a large volume, and then you've got a hot air balloon, not a suit. Combining a smaller volume with a suit designed for air resistance is an interesting idea, but I don't have the knowledge to know how well it would work. Essentially, you have a spectrum from a parachute with huge surface area at one end to a hot air/helium balloon with a huge volume at the other, so I would think that some form of less surface area than a parachute and less volume than a balloon would work. The question is how much less you could get away with.
Also, you mention inflation, implying they aren't inflated to begin with. That complicates things, and probably rules out helium, since where would it come from? Capturing regular air during the fall is possible, but then you need to heat it (and avoid burning your skydiver). 621
Perhaps some chemical lining the empty sacs could trigger a thermal reaction as they fill up, which needs to be replaced every time. This would also prevent long flights or floating off too high, as the heat would run out and you would lose buoyancy.
Last, if your world doesn't need to be too Earth-like, there are factors that would make this more effective. High winds could provide lift to the squirrel suit portion. Lower gravity makes for less force to be fought against in general. A heavier atmosphere would make the air resistance of the squirrel suit work better, plus if you have pre-inflated sacs of a light gas, it would be more effective if the normal air is heavier. Last, and probably least, a colder environment to begin with could make the hot air solution more effective, but I'm not sure how much colder it would need to be to make a significant difference, plus you then need to generate more heat.
Oh, and this whole thing brought to mind the short novel Windhaven by <PERSON> and <PERSON>. 513