What's the minimum distance of focus for the lens of a human eye to reach maximum flatness?
There are practical questions in ophthalmology and you've asked someone that has a common theoretical answer: 6 meters. 

However, you should know that from the same theoretical point the far the object the less accommodation we need, so the second answer is - infinity. 

What is the difference? From the practical point the accommodation between this two points is negligible and does not have to be taken into account when we correct the refraction error.

Small theory - to see an object placed at a distance of 1 meter we need 1D of accommodation power (1/1meter=1D), to see an object placed at a distance of 30cm we need 3D of accommodation power (1/0.3meter=3D), for an object at a distance of 10cm we need 10 diopters and finally for an object at the distance of a 6 meter we need accommodate 0.16 diopter. 

Thus between 6 meter and infinity the accommodation is very low and this is why the distant visual acuity is checked at this distance. Consequently, the lens convexity difference between 6 meters gaze and infinity is negligible and this is why the answer to your question is between 6 meters and infinity (zero accommodation).

From this explanation you can calculate the dioptric add for any reading distance  and understand how the reading spectacles correct the loss of accommodative power (=presbyopia, the vision of older people).

If you want to know how much the crystalline lens changes its dimensions during accommodation, the answer is near 7% for diameter and near 10% for thickness, so the lens as was convex, stays convex and the visible changes are minimal.