We study the effect of radio-jet core shift, which is a dependence of the position of the jet radio core on the observational frequency. We derive a new method of measuring the jet magnetic field based on both the value of the shift and the observed radio flux, which complements the standard method that assumes equipartition. Using both methods, we re-analyse the blazar sample of Zamaninasab et al. We find that equipartition is satisfied only if the jet opening angle in the radio core region is close to the values found observationally, $≃$0.1--0.2 divided by the bulk Lorentz factor, $Γ_{\rm j}$. Larger values, e.g., $1/Γ_{\rm j}$, would imply magnetic fields much above equipartition. A small jet opening angle implies in turn the magnetization parameter of $≪ 1$. We determine the jet magnetic flux taking into account this effect. We find that the transverse-averaged jet magnetic flux is fully compatible with the model of jet formation due to BH spin energy extraction and the accretion being a magnetically arrested disc (MAD). We calculate the jet average mass-flow rate corresponding to this model and find it consists of a substantial fraction of the mass accretion rate. This suggests the jet composition with a large fraction of baryons. We also calculate the average jet power, and find it moderately exceeds the accretion power, $\dot M c^2$, reflecting BH spin energy extraction. We find our results for radio galaxies at low Eddington ratios are compatible with MADs but require a low radiative efficiency, as predicted by standard accretion models. ; Comment: MNRAS, in press