Methinks you misunderstand the purpose of 'flat field'. It has nothing to do with illumination, nothing to do with brightness across the frame.
Flat field correction means that a lens has been specially designed so that if you had a postage stamp adhered to the wall and were attempting to photograph it, all parts of the postage stamp would be in precise focus simultaneous. Contrast 'flat field' surface of a poster vs 'curved field' like the surface of a basketball. As macro lenses were often used to photograph documents, and documents are flat, lens designers needed to ensure that when the lens was focued at very close distances, its focus plane was indeed planar!
I'm not using flat field imaging to adjust geometry for lens distortion. Look up "flat-field correction" and realize I am not convolving a curved field onto a flat plane, just compensating for other aberrations besides geometric lens distortion.



