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