By molecular dymanics simulations we study the spin Seebeck effect as a function of magnetic field in the prototype classical easy-axis antiferromagnetic chain, in the far-out of equilibrium as well as linear response regime. We find distinct behavior in the low field antiferromagnetic, middle field canted and high field ferromagnetic phase. In particular, in the open boundary system at low temperatures, we observe a divergence of the spin current in the spin-flop transition between the antiferromagnetic and canted phase, accompanied by a change of sign in the generated spin current by the temperture gradient. These results are corroborated by a simple spin-wave phenomenological analysis and simulations in the linear response regime. They shed light on the spin current sign change observed in experiments in bulk antiferromagnetic materials.