The problem of determining the collective synchrotron radiation power emitted by non-ideal magnetized plasma fluids at kinetic equilibrium in relativistic jets is addressed. A covariant statistical kinetic approach is implemented based on a novel solution for the corresponding non-isotropic kinetic distribution function (KDF). This is expressed by a Gaussian-like solution that is consistent with relativistic magnetic moment conservation holding in collisionless magnetized plasmas and predicts tensorial equation of state and pressure anisotropy which are specific for these systems. Notably, the same equilibrium admits also a convergent integrable Chapman-Enskog series expansion around a leading-order Juttner distribution, which affords the analytical calculation of continuum fluid fields. In this reference, it is shown that the statistical average of total synchrotron power evaluated over the non-isotropic KDF differs significantly from the corresponding ensemble estimate that would be trivially obtained if the underlying velocity distribution were purely isotropic. It is pointed out that the knowledge of such a statistical discrepancy on the radiation-power curve could provide an independent framework for the characterization of the physical properties of the relativistic plasma state or of the background magnetic field that permeates these astrophysical scenarios.