The other thing you can do to analyze a painting is to record an image of the painting at high-resolution, then perform a 2-D Fourier transform of the image to analyze the spatial frequency content, but this will not reveal an MTF of the painting itself. Spatial frequency content should provide useful information about brush stroke sizes, effects of aging, etc, especially if combined with spectral content analysis.
A painting is not a linear system, a fundamental requirement for an optical transfer function (OTF) and it's corresponding modulus (MTF). Beware of GIGO: Garbage in / garbage out.
If you tried to use the slant-edge method to measure the MTF of an image of a hand-painted edge, then the resultant MTF will simply be that of the camera you imaged the painting with, degraded by the effect of the painted edge not being ideal.