We present an optical and infrared (IR) study of IC 10 X-2, a high-mass X-ray binary in the galaxy IC 10. Previous optical and X-ray studies suggest that X-2 is a Supergiant Fast X-ray Transient: a large-amplitude (factor of ~100), short-duration (hours to weeks) X-ray outburst on 2010 May 21. We analyze R- and g-band light curves of X-2 from the intermediate Palomar Transient Factory taken between 2013 July 15 and 2017 February 14 that show high-amplitude (>~1mag), short-duration (<~8days) flares and dips (>~0.5mag). Near-IR spectroscopy of X-2 from Palomar/TripleSpec show He I, Paschen-{gamma}, and Paschen-{beta} emission lines with similar shapes and amplitudes as those of luminous blue variables (LBVs) and LBV candidates (LBVc). Mid-IR colors and magnitudes from Spitzer/Infrared Array Camera photometry of X-2 resemble those of known LBV/LBVcs. We suggest that the stellar companion in X-2 is an LBV/LBVc and discuss possible origins of the optical flares. Dips in the optical light curve are indicative of eclipses from optically thick clumps formed in the winds of the stellar counterpart. Given the constraints on the flare duration (0.02-0.8 days) and the time between flares (15.1+/-7.8days), we estimate the clump volume filling factor in the stellar winds, f_V_, to be 0.01<f_V_<0.71, which overlaps with values measured from massive star winds. In X-2, we interpret the origin of the optical flares as the accretion of clumps formed in the winds of an LBV/LBVc onto the compact object.