ASASSN-14ko is a recently discovered periodically flaring transient at the center of the active galactic nucleus (AGN) ESO 253-G003 with a slowly decreasing period. Here, we show that the flares originate from the northern, brighter nucleus in this dual-AGN, post-merger system. The light curves for the two flares that occurred in 2020 May and September are nearly identical over all wavelengths. For both events, Swift observations showed that the UV and optical wavelengths brightened in unison. The effective temperature of the UV/optical emission rises and falls with the increase and subsequent decline in the luminosity. The X-ray flux, by contrast, first rapidly drops over ~2.6 days, rises for ~5.8 days, drops again over ~4.3 days, and then recovers. The X-ray spectral evolution of the two flares differ, however. During the 2020 May peak the spectrum softened with increases in the X-ray luminosity, while we observed the reverse for the 2020 September peak. We found a small change in the period derivative, which seems to indicate that the system does not have a static period derivative and there is some stochasticity in its evolution.