Magnetorheological particles, permanently linked into chains, provide a magnetically actuated means to manipulate microscopic fluid flow. Paramagnetic colloidal particles form reversible chains by acquiring dipole moments in the presence of an external magnetic field. By chemically connecting paramagnetic colloidal particles, flexible magnetoresponsive chains can be created. We link the paramagnetic microspheres using streptavidin-biotin binding. Streptavidin coated microspheres are placed in a flow cell and a magnetic field is applied, causing the particles to form chains. Then a solution of polymeric linkers of bis-biotin-poly(ethylene glycol) molecules is added in the presence of the field. These linked chains remain responsive to a magnetic field; however, in the absence of an external magnetic field these chains bend and flex due to thermal motion. The chain flexibility is determined by the length of the spacer molecule between particles and is quantified by the flexural rigidity or bending stiffness. To understand the mechanical properties of the chains, we use a variety of optical trapping experiments to measure the flexural rigidity. Increasing the length of the poly(ethylene glycol) chain in the linker increases the flexibility of the chains.