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.