The next generation BLAST experiment (BLAST-TNG) is a suborbital balloon payload that seeks to map polarized dust emission in the 250 $mu$m, 350 $mu$m and 500 $mu$m wavebands. The instrument utilizes a stepped half-wave plate to reduce systematics. The general requirement of the detectors is that they are photon-noise-limited and dual-polarization sensitive. To achieve this goal, we are developing three monolithic arrays of cryogenic sensors, one for each waveband. Each array is feedhorn-coupled and each spatial pixel consists of two orthogonally spaced polarization-sensitive microwave kinetic inductance detectors (MKIDs) fabricated from a Ti/TiN multilayer film. In previous work, we demonstrated photon-noise-limited sensitivity in 250 $mu$m waveband single polarization devices. In this work, we present the first results of dual-polarization sensitive MKIDs at 250 $mu$m.