We study electron transport through a serial double quantum dot with Rashba spin-orbit interaction (SOI) and Zeeman field of amplitude B in the presence of local Coulomb repulsion. The linear conductance as a function of a gate voltage Vg equally shifting the levels on both dots shows two B=0 Kondo ridges, which are robust against SOI as time-reversal symmetry is preserved. As a result of the crossing of a spin-up and a spin-down level at vanishing SOI, two additional Kondo plateaus appear at finite B. They are not protected by symmetry and rapidly vanish if the SOI is turned on. Left-right asymmetric level-lead couplings and detuned on-site energies lead to a simultaneous breaking of left-right and bonding-antibonding state symmetry. In this case, the finite-B Kondo ridges in the Vg-B plane are bent with respect to the Vg axis. For the Kondo ridge to develop, different level renormalizations must be compensated by adjusting B.