The nuclear transient AT2019cuk/Tick Tock/SDSS J1430+2303 has been suggested to harbor a supermassive black hole (SMBH) binary near coalescence. We report results from high-cadence NICER X-ray monitoring with multiple visits per day from 2022 January to August, as well as continued optical monitoring during the same time period. We find no evidence of periodic/quasiperiodic modulation in the X-ray, UV, or optical bands; however, we do observe exotic hard X-ray variability that is unusual for typical active galactic nuclei (AGN). The most striking feature of the NICER light curve is repetitive hard (2-4 keV) X-ray flares that result in distinctly harder X-ray spectra compared to the nonflaring data. In its nonflaring state, AT2019cuk looks like a relatively standard AGN, but it presents the first case of day-long, hard X-ray flares in a changing-look AGN. We consider a few different models for the driving mechanism of these hard X-ray flares, including (1) corona/jet variability driven by increased magnetic activity, (2) variable obscuration, and (3) self-lensing from the potential secondary SMBH. We prefer the variable corona model, as the obscuration model requires rather contrived timescales and the self-lensing model is difficult to reconcile with a lack of clear periodicity in the flares. These findings illustrate how important high-cadence X-ray monitoring is to our understanding of the rapid variability of the X-ray corona and necessitate further high-cadence, multiwavelength monitoring of changing-look AGN like AT2019cuk to probe the corona-jet connection.