There are relatively few observations of UV emission during the impulsive phases of solar flares, so the nature of that emission is poorly known. Photons produced by solar flares can resonantly scatter off atoms and ions in the corona. Based on off-limb measurements by the Solar and Heliospheric Observatory/Ultraviolet Coronagraph Spectrometer, we derive the O VI λ 1032 luminosities for 29 flares during the impulsive phase and the Lyα luminosities of 5 flares, and we compare them with X-ray luminosities from GOES measurements. The upper transition region and lower transition region luminosities of the events observed are comparable. They are also comparable to the luminosity of the X-ray emitting gas at the beginning of the flare, but after 10-15 minutes the X-ray luminosity usually dominates. In some cases, we can use Doppler dimming to estimate flow speeds of the O VI emitting gas, and five events show speeds in the 40-80 km s-1 range. The O VI emission could originate in gas evaporating to fill the X-ray flare loops, in heated chromospheric gas at the footpoints, or in heated prominence material in the coronal mass ejection. All three sources may contribute in different events or even in a single event, and the relative timing of UV and X-ray brightness peaks, the flow speeds, and the total O VI luminosity favor each source in one or more events.