We examine experimentally the deformation of flexible, microscale helical ribbons with nanoscale thickness subject to viscous flow in a microfluidic channel. Two aspects of flexible microhelices are quantified: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive-force theory. The deformation of helices by viscous flow is well described by nonlinear finite extensibility. Under distributed loading, the pitch distribution is nonuniform, and from this we identify both linear and nonlinear behavior along the contour length of a single helix. Moreover, flexible helices are found to display reversible global to local helical transitions at a high flow rate.