For oil painting natural light is ideal.
For painting it, yes. For viewing it, yes. For photographing it, no way.
Not that no accident will ever happen in a studio but shooting outdoors is way more dangerous. And considering the value of some paintings I can't imagine any photogs, in his or her right mind, shooting outside. Sorry.
To the OP: Shooting art work is a very specialized form of photography and certainly not the easiest. I am a photographer with over 30 years of experience. I am also a painter in need of photos fairly regularly. I very rarely shoot those photos myself. Mind you, I'm sure I could learn and so can you but it is not going to be instant.
I don't know what your level is as a photog and there is no better way to learn than by doing but be ready for some massive headaches.
As mentioned, the sensor plane needs to be parallel to the art work. Absolutely 100% so.
Also as mentioned, your colors need to be spot on. Not on your monitor but checked against a color scale.
Another thing that was mentioned was lighting evenly. Although that is true, it is only so to a degree. Paintings may not be quite flat, plenty of them have quite a huge amount of texture to them and depending on what you are shooting for, this may need to be shown. To some extent.
If I think of anything else I will come back.