IGR J08408-4503 is a supergiant fast X-ray transient discovered in 2006 with a confirmed association with a O8.5Ib(f) supergiant star, HD 74194. We report on the analysis of two outbursts caught by Swift/BAT on 2006 October 4 and 2008 July 5, and followed up at softer energies with Swift/XRT. The 2008 XRT light curve shows a multiple-peaked structure with an initial bright flare that reached a flux of ~1E-9 erg/cm2/s (2-10 keV), followed by two equally bright flares within 75 ks. The spectral characteristics of the flares differ dramatically, with most of the difference, as derived via time-resolved spectroscopy, being due to absorbing column variations. We observe a gradual decrease of the NH, derived with a fit using absorbed power law model, as time passes. We interpret these NH variations as due to an ionization effect produced by the first flare, resulting in a significant decrease in the measured column density towards the source. The durations of the flares, as well as the times of the outbursts suggest that the orbital period is ~35 days, if the flaring activity is interpreted within the framework of the Sidoli et al 2007 model with the outbursts triggered by the neutron star passage inside an equatorial wind inclined with respect to the orbital plane.