To elaborate further, is it possible to fly if a creature has the wing structure of a bat, but instead of membranous skin, they have feathers?
Feathers don't need fingers.
The bat uses the tips of its "fingers" to anchor the far side of the flight membrane. We will call the fingers vertical and the membrane horizontal because that is how it is in this picture. For a bird, all the feathers are vertical elements. Having some vertical fingers in among them does not really help the feathers do what they do; the creature would be better off with another feather.
Maybe what you want is a scansoriopterygid!
Scansoriopterygids differentiate from other theropod dinosaurs in part by their extremely long third fingers, which were longer than the first and second digits of the hand. In all other known theropods, the second finger is the longest. At least two species, Yi and Ambopteryx, also had a long "styliform" bone growing from the wrist, which, along with the third finger, helped support a bat-like wing membrane used for gliding. This use of a long finger to support a wing membrane is only superficially similar to the wing arrangement in pterosaurs, even though it is physically more bat-like....
Yi also preserves feathers. These are notably very simple for a member of Pennaraptora (a clade of which scansoriopterygids are usually considered members), being "paintbrush-like", with long quill-like bases topped by sprays of thinner filaments. The feathers covered most of the body, starting near the tip of the snout. The head and neck feathers were long and formed a thick coat, and the body feathers were even longer and denser, making it difficult for scientists to study their detailed structure.
John Dailey proposed a question here that I liked about scaling up these ancient fliers. How CAN a Wyvern be a Scansoriopterygid Dinosaur?
Maybe your bat winged dragon with feathers could be one of these?
I'm not sure this is possible. Bat wings fly with a very different movement compared to bird wings. A bird's wing moves rather like a human flapping their arms up and down: there's little flexibility of movement, so stiff feathers work to maintain a reasonably consistent flight profile without gaps in the wing surface. A bat, on the other hand, should have its wing compared to a human hand instead: most of the wing surface is the membrane between the fingers, and manipulating the shape of that membrane is how they control their flight.
I'm not entirely certain on this, but putting feathers on a bat wing means the surface is no longer connected to itself; I'm drawing a blank on how best to describe it, but it's no longer a continuous surface. As the wings flap, gaps will open up where the feathers would come together, gaps that will seriously distort airflow and steal a lot of lift or cause drag, and this is going to be harder to patch up as you increase the scale towards dragon-sized. You don't see this effect on bird wings because their movement is mostly simple up-and-down, at least not intact ones: a damaged wing with feathers missing or ruined will lose lift disproportionate to the loss of feathers, since a small cavity or gap can have a big impact. Bat wings move around a lot more to manage their flight, and using feathers as the flight surface instead of skin would rob them of effective control.
Thus, my verdict is that feathered bat wings are likely to fail (or at least be far less effective than either bat wings or bird wings in isolation) because they won't be good at stable flight. It might be possible to circumvent the airflow problems and other difficulties, but that's going to take a lot of energy and effort and be generally inefficient, so there's no reason to go this route.