This is something I’m thinking about. Now, these would be wings that are not powered by the person themself, since we do not have the strength for it (and I don’t want to use legs). They’d be powered by a battery, and have a set of movements coded. Left, right, gliding, sensors, everything. Made out of the most light-weight materials. Now, humans are heavy, yes, but with properly designed wings for our body shape and weight, do you believe this is possible?
Hummingbird drone wings.
Bird wings that work by flapping / gliding need to scale up with body size. That is covered in this question. How big would my character's wings realistically be?. For a human, condor-style wings would be super large and ungainly.
But hummingbirds use their wings in a different way - sculling the air at high speeds. I suspect that hummingbird style flight does not scale up because higher forces required for heavier bodies put stresses on the skeleton beyond what bone and ligament can withstand.
Not beyond what titanium and carbon fiber can withstand. Your character's small artificial wings scull the air like a hummingbird, allowing her to hover and dart about. The hummingbird drone beats its wings at 30 times a second. The artificial wings go much faster.
I would recommend your character keep her hair cut short, or wear a helmet.
A mechanical device intended for a person to fly is a manned aircraft, and a few of them fly by flapping wings. They are called ornithopters.
However, flapping wings doesn't result practical nor efficient for a mechanical device and the only ornithopters that have been developed until having some practical application have been very small unmanned ones where looking like a bird or an insect is an advantage - like the examples in Willk's answer.
When dealing with something that flies the core problem is the power / weight ratio. You must have enough power to use your wings to create enough lift but usually, with current technologies, more power also means more weight.
They’d be powered by a battery,
So the question is: how much power can this battery produce? How much does it weight?
I have built several multicopters and that is always the focal issue. Currently there is not a suitable battery for your mechanical wings.
BUT technology evolves. 20 years ago we could only dream of the kind of lipo batteries we are using today. Research is very active in evolving batteries technology. Patents in this field could yield trillions from multiple sectors (automobiles, power tools, drones, robots, laptops, tablets, smartphones, etc).
So if your setting is in the not so near future then I would say that most likely that technology will be reality.
Personally I would imagine wings for personal human use more similar to those of an insect than those of a bird. You could read this: The nature of flight
However, despite recent research into the flight of bats and hummingbirds, arguably the most exciting insights have come from flying insects, in particular about the structure of the flight muscles and their coordination with the central nervous system.
A secondary aspect of your flying wings would be how to control them. I would imagine some kind of AI. You don't really need something extremely refined, just enough to read patterns of behavior to adapt the control of the wings to the user input. The user should not have to micro-manage the control of the wings.