Planck's constant was measured. It cannot be derived.
Specifically, it comes from the deBrogile relationships, which state that for elementary particles, the following relationships hold.
$$E = \hbar \omega$$
$$p = \hbar k$$
Here, $E$ represents energy, $p$ represents momentum, $\omega$ represents angular frequency, and $k$ represents wavenumber. So, if you can take a photon (particle of light) and measure its angular frequency $\omega$ (i.e. - its color) and then also measure its energy $E$, you can compute Planck's reduced constant $\hbar = E / \omega$.
These deBrogile relationships were stated after scientists noticed that there was a linear relationship between $E$ and $\omega$ as well as $p$ and $k$ for elementary particles (and incidentally,their constant of proportionality $\hbar$ ends up being the same for both relationships--this is not obvious--only can be determined by experiment!). Once you have the equations, you can then measure the value of $\hbar$.