Xjyuk

Answers to this question note that human (and by extension mammal) wings would use naked skin instead of feathers, as we see on bats. However, with feathers, birds can have wings with shaped more like those of an aircraft (often with bell-shaped spanload, it seems), which is more efficient than a flat surface for generating lift, without adding as much weight as would flesh. In comparison, bat wings are very flat.

Would having inflatable air bladders under the skin, in order to give a similar shape, be beneficial for generating lift? Or would the gains be too marginal to be worth it for a flying mammal?

Some answers to this question note that bat wings are more agile, at the cost of being less efficient for generating lift. The idea here would be to compromise differently and have better gliding wings.

It would have benefits to lift, but they'd be very susceptible to damage.

Adding air-filled bladders to a wing to make it more aerodynamic would be a lightweight solution to adding lift compared to adding supporting structures so there would be benefit to it.

Issue 1: damage

However, skin wings are already more susceptible to damage than feathered ones. The loss of even a number of individual feathers does not necessarily ground a bird, but damage to a bat's wing is easily exacerbated into a full tear through use. As a response to this, bat wings have evolved to be some of the fastest healing mammalian tissue structures.

If you are relying on the aerodynamic shape of an air-filled bladder on a wing to generate enough lift to fly, then damage to that structure is pretty risky. If a bladder becomes even slightly punctured it will deflate and ruin your aerodynamics. You may still be able to fly using a deflated wing, but evolution tends towards efficiency so it is more likely that any small injury would result in the animal being grounded until it heals and inflates again.

This doesn't necessarily mean that the trade-off isn't worth it, but the benefits are looking pretty thin.

Issue 2: alternative solutions

The usual solution to gaining more lift is to evolve bigger wings. Either longer or broader, depending on your flight strategy. There are drawbacks to this (higher wing-loadings, lower manoeuvrability, and more weight), but it is also quite an easy thing to evolve compared to novel structures within a wing.

Smaller wings are better for manoeuvrability and lighter weight. They tend to be selected for in environments where animals have to fly around hazards like branches or predators.

The issue we have with bladder-wings is that what we're after is high-lift small wings. Unfortunately, as these are typically a response to hazardous environments, a solution that is very susceptible to damage is not a great solution.

Add together inefficient solution and difficult to evolve and it's not hard to see why it hasn't occurred in nature thus far.

So, how can we make this plausible?

Perhaps, what we want is a situation where simply increasing wingspan isn't enough. We also want a situation where lift is at a premium over manoeuvrability, and risk of damage is low.

Maybe your bladder-wing bats are pelagic sea gliders like albatrosses.

If you're big enough, there's not a great deal out above the open ocean that will damage your wings, and lift is most certainly at a premium if you want to fly vast distances. There have been pterasaurs with very large wingspans so it is possible to have very big skin wings.

So, they'd probably just evolve really big wings like pterasaurs and albatrosses. Drat.

Hang on...we might be able to get this to work...

There are some key trade-offs for animals that both fly and swim. The one we're interested in is the relative wing-loadings of animals that use their wings to swim.

As water is so much more dense than air, you need a lot stouter wings to swim well in it. There's a trade-off between ability to swim underwater and fly in the air. Puffins have tiny wings and very inefficient flight in order to be able to swim very well underwater. Flightless penguins are the logical extreme of this.

If an albatross flapped its massive wings underwater it would break its bones. As such it's unable to dive, and is relegated to a feeding strategy where it attracts squid to the surface at night. It works (evidently), but there's a lot of resources albatrosses can't exploit.

This sets up the right set of pressures to favour high-lift short wings. If your bladder-bats are able to deflate their bladders to decrease their buoyancy, they might be able to travel vast distances at sea efficiently and dive well enough to hunt beneath the surface of the water. They also avoid the trade-off of water-repellent feathers trapping air and increasing buoyancy so might be better divers than birds.

They might actually be able to compete well enough with albatrosses (and other diving pelagic birds like shearwaters) to plausibly survive in the wild!

tl;dr The only plausible set of environmental pressures I can see for bladder-winged bats comes from long-distance flying diving pelagic sea-birds.

At the scale of a bat (normally not much bigger than a house mouse, maximum about the weight of a large rat) the cross section of the airfoil makes much less difference that it would with something that weighs, for instance, what a large hawk or albatross does.

In fact, the bat's thin wing has a much thicker bone "spar" near the leading edge, and a deeply cambered surface behind; this is actually a very efficient shape for a small (low Reynolds number), low-loading surface. To compare, look at the difference between the wings of small hand launched gliders (typical span 30-45 cm, weight comparable to a small bat) and those of larger model sailplanes (spans 1.5 to 3 m, weight 1-5 kg).

The hand launch gliders have very thin wings, and in fact often little camber; this latter is because they need to fly at very high speed when launched, but the designs that have used built-up wings to add thickness have not generally done enough better in competition to take over from the thin solid sheet wing construction. It's also common for indoor hand launch gliders to have flexible cambered surfaces -- the camber "blows flat" during the high speed launch, then flexes back like a flap to increase lift and change stability during the glide. In final configuration, the result is much like the inner panel of a bat's wing (inboard of the "pinkie finger" bone).

Therefore, in considerable of the relative fragility of an air bladder (as mentioned in another answer) and the questionable aerodynamic advantage of a thicker wing over a thin, cambered one in this flight regime, it seems unlikely that such a feature would provide enough advantage to evolve naturally.