Worked with him on the latest stuff so know a bit about it.
He's using vertex shaders to make the visual adjustments and injecting into the AC exe (or anyway reading its calls) to find pointers for the physics data to make those adjustments.
On the physics side, the vertical flex is just the tire radius in the data files (static radius) minus current radius (active radius). He then redraws the tire based on that.
Lateral flex is a bit different as there's more going on. To do it properly, you'd really need some extra data in the physics (such as lateral spring rate), so it's somewhat fudged. That said, the data I've seen for lateral spring rate is actually quite similar to that of vertical spring rate, so I used that when writing the equation. Overall it's rather simple; lateral force divided by vertical spring rate multiplied by a constant. The constant is a somewhat arbitrary "technology factor" based on the flex parameter in the data files for the tires. It attempts to account for differences in construction between different tires.
edit: forgot longitudinal. Longitudinal is the same as lateral flex but it uses longitudinal forces (obviously) and the CX_MULT parameter when available.