Single crystal Sb2Te3 topological insulator nanoflakes with the thickness of 25 nm and 456 nm were synthesized via vapor phase deposition method. The Hall resistance and magnetoresistance of the nanoflakes have been measured at temperatures 2 K and 300 K in the fields up to 9 T. The magnetoresistance and Hall resistance of the nanoflakes demonstrate significant differences, so that despite ordinary magnetoresistance and Hall effect obtained for 25 nm sample 450 nm nanoflake demonstrates unusual magnetoresistance and nonlinear Hall resistance. The sense of curvature of both Rxx(B) and Rxy(B) dependences is inversed at high temperature. The experimental data have been analyzed in the frame of a multichannel transport model. The difference in the behavior is attributed to the existence of the charge carriers with high and low mobility, as well as to their relative contribution (which varies depending on the temperature) to the magneto-transport of the nanoflakes.