How I determine numerically the roll rate of an aircraft?
In order to determine the roll rate of an aircraft, all you need to do is to set the rolling moment from aileron deflection equal to the roll damping of the wing (actually, of the whole aircraft, but the wing dominates roll damping anyways). So you set
$$c_{l\xi}\cdot\frac{\xi_{left}-\xi_{right}}{2} = -c_{lp}\cdot p = -c_{lp}\cdot\frac{\omega_x\cdot b}{2\cdot v_{\infty}}$$
$$\Rightarrow\omega_x = -\frac{2\cdot v_{\infty}}{b}\cdot\frac{c_{l\xi}}{c_{lp}}\cdot\frac{\xi_{left}-\xi_{right}}{2}$$

The symbols are:
$\kern{5mm} \xi\:\:\:\:\:$ aileron deflection angle
$\kern{5mm} v_{\infty}\:\:$ velocity
$\kern{5mm} b\:\:\:\;$ wing span
$\kern{5mm} c_{lp} \:\:$  coefficient of roll damping, using $\frac{b}{2}$ for its reference length
$\kern{5mm} c_{l\xi} \:\;$ coefficient of rolling moment due to aileron deflection
$\kern{5mm} p \:\:\:\;$ dimensionless roll rate
$\kern{5mm} \omega_x \:\:$  rolling speed in rad/sec

Damping decreases with altitude, and in this equation the increase of flight speed with altitude will make sure that roll damping decreases accordingly.