[Na Horuk]

You can look at websites like Photozone or Lenstip or DXoMark, find your lens, and then check the zoom range with the lowest distortion. DA 18-55mm reaches lowest distortion when zoomed around 40-55mm, if I remember right, so it was a good choice
Avoid "shooting up" at an angle. Like I said earlier, sensor has to be PARALLEL in ALL directions. Photographing still life, making copies of documents, and slide copying is all about the setup. You have to make the conditions that will allow you to get a good shot. Otherwise part of the painting will look oddly crooked. This also goes for most of other types of photography, like street, landscapes, architecture, even portraits. Some people buy a little waterscale accessory that fits into the hotshoe, and some tripods have one built in. And some cameras have a type of 'horizon level' function. These are great, as long as the subject is not crooked (and things like crooked walls are more common that you might think!)

Someone earlier said primes still have distortion - true, but as a rule, they have less of it than zoom lenses of similar cost, particularly if the zoom is set to shortest or longest FoV. This is also why I recommended the DA 50mm over the DA 35mm. And why DFA 50mm is best for such purposes. Sharp, flat field of focus, practically no distortion, and amazing working distance. You can get really really close to the painting, up to 1:1 magnification. But still, just get the painting to be perfectly in front of the camera, with verticals and horizontals lining up, and the photo will already look better. Once you learn to do this with one painting, you will have a setup you can use for all other painting shots, so its worth it to take some time and make it as close to perfect as you can.

[SpecialK]

Being level is helpful, but I was suggesting you make sure the edges of the frame are actually straight lines. The frame looks thin, and if it's being hung by a single point near the centre top, it may bend the top frame as SpecialK has mentioned.

Yes, that is the point, and seems to be the problem as the other 3 sides look fine.

Here's a shot with a prime (DA 21). Not good.

[Schraubstock]

From the photo it is obvious the camera sensor was not parallel to the painting canvas. This means the distortion of the lens and perspective will be exaggerated.

Parallax !
This why you can sometimes observe professional interior or real estate photographers standing on a light portable 4 or five rung step ladder (and even use a super high tripod when standing on the ladder) rather than using at tilt and shift lens. The result is better.

Going on a holiday with a step ladder in order to photograph buildings without falling lines is not so good though. Corrections in PP will be the better option

[Na Horuk]

Here's a shot with a prime (DA 21). Not good.

But DA 21mm is a special case. It is designed for completely other priorities than taking photos of paintings. It is a pancake lens, with low aperture, it is wide angle. Yes, it has distortion. But I wouldn't recommend using a lens wider than 35mm for reproduction/documentary purposes. Even the DA 35mm f2.4 has some distortion. The limited DA 35mm f2.8 macro is better. Something in the range of 50-85mm would be better still. I don't think anyone here is recommending the DA 21mm as a great lens for this purpose (I quite like the DA 21mm, though! For landscapes, nature, street, city.. Great colors and contrasts, super compact for travel)
Of course some lenses are better suited than others. But to get the best distortion characteristics you would use a normal or short telephoto macro prime. Working distance is important, as well. Shooting from really up close will always exaggerate lines, even if the lens itself would have highly corrected distortion. And by definition, wide angle lenses will be used at a closer distance than telephoto.
So, OP using 18-55mm at around 50mm+ or using a 70-200mm around 70-85mm are decent choices. Using aperture of around f8 and ISO 100 are good, too. 2sec timer and EV +/- (to add a touch of brightness) would nail it. But the main problem in OP's question is distortion (can be minimized with right lens and good digital PP) and the lens not being aligned with the painting.
SpecialK's example is using a lens with notorious distortion and it doesn't look that terrible, because the setup was good. Now, using the right lens with that setup would be perfecto.

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Last edited by Na Horuk; 01-18-2017 at 06:10 AM.

[SpecialK]

But DA 21mm is a special case.

At least 2 posters generically said "use a prime", not a good prime :-)

[Na Horuk]

At least 2 posters generically said "use a prime", not a good prime :-)

Sure, but you don't want to overwhelm a thread by writing a two page essay about which primes are suited for which tasks, and which zooms are good and which are bad, and which are the exceptions. I'm sure you can find some bad 50mm primes out there, if you look hard enough. But it is still okay to give a general recommendation that 50mm are affordable lenses with high quality rendering.
And the DA 21mm is a good prime! Just not the best for that specific task. But yeah, you made your point