The way I have modelled this in CAD is to assume that only the narrow 3mm-thick parts of the milled piece can bend. That is, the bits between the engraved lines don’t bend at all. That leaves figuring out how much the top and bottom faces of the 3mm-thick parts will bend under pressure.
My first attempt happened to work, so I did all my kerfing in these chairs with these same dimensions.
If we zoom in on these thin 6.35 mm-wide, 3 mm-thick areas of the piece, then what I have found to work is to assume that the face under compression will narrow to 6.27 mm, and the face being stretched will expand to 6.43 mm. I have spaced out the pieces here for you see: