Antiferromagnets may exhibit spin superfluidity since the dipole interaction is weak. We seek toestablish that this phenomenon occurs in insulators such as NiO, which is a good spin conductor accordingto previous studies. We investigate nonlocal spin transport in a planar antiferromagnetic insulator witha weak uniaxial anisotropy. The anisotropy hinders spin superfluidity by creating a substantial thresholdthat the current must overcome. Nevertheless, we show that applying a high magnetic field removes thisobstacle near the spin-flop transition of the antiferromagnet. Importantly, the spin superfluidity can thenpersist across many micrometers, even in dirty samples.