The protein fibrin plays a principal role in blood clotting and forms robust three dimensional networks. Here, microfluidic devices have been tailored to strategically generate and study these bionetworks by confinement in nanoliter volumes. The required protein components are initially encapsulated in separate droplets, which are subsequently merged by electrocoalescence. Next, distinct droplet microenvironments are created as the merged droplets experience one of two conditions: either they traverse a microfluidic pathway continuously, or they "park" to fully evolve an isotropic network before experiencing controlled deformations. High resolution fluorescence microscopy is used to image the fibrin networks in the microchannels. Aggregation (i.e."clotting") is significantly affected by the complicated flow fields in moving droplets. In stopped-flow conditions, an isotropic droplet-spanning network forms after a suitable ripening time. Subsequent network deformation, induced by the geometric structure of the microfluidic channel, is found to be elastic at low rates of deformation. A shape transition is identified for droplets experiencing rates of deformation higher than an identified threshold value. In this condition, significant densification of protein within the droplet due to hydrodynamic forces is observed. These results demonstrate that flow fields considerably affect fibrin in different circumstances exquisitely controlled using microfluidic tools.