Are there collected data about the direction of rotation of black holes and the direction of the magnetic field?
For pulsars the relation is complex. The magnetic field tends to "freeze in place" after the star collapses, but I'm sure there are all kinds of perturbation mechanisms that may change its initial orientation.

For blackholes (the Kerr-Newman metric, rotating and charged black hole) the relation is very simple: the rotation axis of the BH and the symmetry axis of its magnetic field always coincide.

https://en.wikipedia.org/wiki/Kerr%E2%80%93Newman_metric#Some_aspects_of_the_solution

There is a simple and intuitive justification, although perhaps not rigorous. If the magnetic field was not aligned with rotation, the BH would appear to be "blinking". But a BH cannot "blink", nor can it otherwise send any signals to the external universe. Therefore, its magnetic field axis must coincide with its rotation axis.