We investigate the nonlinear optical properties of BiOBr nanoflakes - a novel two-dimensional (2D) layered material from the bismuth oxyhalide family. We measure the nonlinear absorption and Kerr nonlinearity of BiOBr nanoflakes at both 800 nm and 1550 nm via the Z-Scan technique. We observe a large nonlinear absorption coefficient β ∼10-7 m/W as well as a large Kerr coefficient n2 ∼10-14 m2/W. We also observe strong dispersion in n2, with it reversing sign from negative to positive as the wavelength varies from 800 nm to 1550 nm. In addition, we characterize the thickness-dependence of the nonlinear optical properties of BiOBr nanoflakes, observing that both the magnitudes of β and n2 increase for very thin flakes. Finally, we integrate BiOBr nanoflakes onto silicon integrated waveguides and characterize the linear optical properties of the resulting hybrid integrated devices, with the measurements agreeing with calculated parameters using independent ellipsometry measurements. These results verify the strong potential of BiOBr as an advanced nonlinear optical material for high-performance hybrid integrated photonic devices.