Flaking will be down to bad prep and/or brittle paint. I'd use a 2K on wheels and acrylic on centre caps (because of its slightly better plasticity). You could probably use acrylic on the wheels too without issue, but 2K is a bit more durable and probably less vulnerable to brake dust, just guessing there.
If I do one of these wheels this afternoon, it will be with a compressor and acrylic, but just as I have described below for spraypaks... not willing to spend a lot of time on it lol
If you are doing a home job and dont have spray equipment, I think I would give acrylic spraypaks a go. You can buy them at supercheap, just read the label. Hey, if it doesnt work, the wheels are cheap to replace..
If you are going to use spraypaks, then less is best. Dont go overboard with preparation, trying to remove all old paint and blemishes. You dont want to remove the old paint or then you need to start worrying about etch primer etc..
Just thoroughly clean every nook and cranny of the wheel with a small brush and wax&grease remover. Then rub it all back with 800G wet and dry, rubbing wet. Then again with the wax&grease remover and brush. Wipe off all residue, polish that sucker dry. Then hit it with your black spraypaks.
First get the nooks and crannys. A quick squirt into all the hard to get at places, making sure to keep the edges feathered. Then the same again, increasing the area. Then a light coat over the whole wheel, not trying to get full coverage. Do it again, you should have full coverage this time. Then a single wet coat over the lot.
Just use a base paint, dont bother with clear over base. This isnt going to be perfect either, but it should look ok and be reasonably easy to do.
Unless you get down to metal, etch prime etc, and use the right paints and processes on the wheel, it will have a limited life span anyway. You will probably be re-doing it every couple years.
Its just acrylic. You could get a similar result with care from aerosol cans, because finish isnt critical. The shapes of the wheel are pretty forgiving when it comes to mistakes.
You can walk into any shop that stocks automotive paint to buy it, but you will need a spraygun and compressor as well of course, or you can use aerosol cans from supercheap, they stock acrylic aerosols.
If you think you might want to paint other things later, then your own gun and compressor will give you a better job and better colour matches at a fraction of the (paint) price long term. Those aerosols arent too bad to use and pretty foolproof, but very expensive compared to buying tins of paint. Ultimately the finish is inferior to what you can get yourself with a decent gun and some practice too.
You only need plastic primer if you rub through the original silver to the plastic on the centre cap. You only need etch primer if you rub through to the alloy of the wheel.
Just rub it back, undercoat it with an acrylic primer/filler, then rub it back smooth and spray the black on, as described in my earlier post. You could then leave it at that, or for that 'wet' look, rub the black back smooth and lay some clear over the top.
For this job, because its not something I particularly cared about I didnt bother doing anything, just cleaned it and sprayed it black. As you can see, it looks fine, but the lack of sanding and primer means it probably wouldnt last long on a car.
With primer properly applied, it would be fine though. I wouldnt see the need for a clear coat personally. Unless you get the wheel powder coated, you will be touching up the wheels regularly no matter what paint you use.