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We investigate the correlation between rest-frame UV flux variability of broad absorption line (BAL) quasars and their variability in BAL equivalent widths (EWs) in a various timescale from $<10$~days to a few years in the quasar rest-frame. We use the data sets of BAL EWs taken by the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project and photometric data taken by the intermediate Palomar Transient Factory (iPTF) in $g$ and $R$-bands and the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) in $grizy$ bands. Our results are summarized as below; (1) the distributions of flux variability versus BAL variability show weak, moderate, or a strong positive correlation, (2) there is no significant difference in flux variability amplitudes between BAL quasar with significant short timescale EW variability (called class S1) and without (class S2), (3) in all time scales considered in this paper, the class S1 quasars show systematically larger BAL variability amplitudes than those of the class S2 quasars, and (4) there are possible correlations between BAL variability and physical parameters of the quasars such as black hole masses (moderate positive), Eddington ratios, and accretion disk temperature (strong negative) in the class S2 quasars. These results indicate that the BAL variability requires changing in the ionizing continuum and an ancillary mechanism such as variability in X-ray shielding gas located at the innermost region of an accretion disk.