We study chromospheric oscillations including umbral flashes and running penumbral waves in a sunspot using scanning spectroscopy in H-alpha and Ca II 8542A, with the Fast Imaging Solar Spectrograph (FISS) at the 1.6 meter New Solar Telescope at Big Bear Solar Observatory. A bisector method is applied to spectral observations to construct chromospheric Doppler velocity maps. Temporal sequence analysis of these shows enhanced high-frequency oscillations inside the sunspot umbra in both lines. Their peak frequency gradually decreases outward from the umbra. The oscillation power is found to be associated with magnetic-field strength and inclination, with different relationships in different frequency bands.