We propose a strategy for optimizing distribution of flow in a microfluidic chamber for microreactor, lateral flow assay and immunocapture applications. It is aimed at maximizing flow throughput, while keeping footprint, cell thickness, and shear stress in the distribution channels at a minimum, and offering a uniform flow field along the whole analysis chamber. In order to minimize footprint, the traditional tree-like or "rhombus" design, in which distribution microchannels undergo a series of splittings into two subchannels with equal lengths and widths, was replaced by a design in which subchannel lengths are unequal, and widths are analytically adapted within the Hele-Shaw approximation, in order to keep the flow resistance uniform along all flow paths. The design was validated by hydrodynamic flow simulation using COMSOL finite element software. Simulations show that, if the channel is too narrow, the Hele-Shaw approximation loses accuracy, and the flow velocity in the chamber can fluctuate by up to 20%. We thus used COMSOL simulation to fine-tune the channel parameters, and obtained a fluctuation of flow velocity across the whole chamber below 10%. The design was then implemented into a PDMS device, and flow profiles were measured experimentally using particle tracking. Finally, we show that this system can be applied to cell sorting in self-assembling magnetic arrays, increasing flow throughput by a factor 100 as compared to earlier reported designs.