We investigate the dynamics of sedimenting Brownian filaments using experimental, computational, and theoretical approaches. The filaments under consideration are composed of linked colloidal particles that form bead-spring-like chains. Under the action of gravitational forces, the nonlocal hydrodynamic interactions cause the filaments to bend and rotate to get their end-to-end direction perpendicular to gravity. Different reorientation mechanisms are verified for different regimes of flexibility, characterized by the elastogravitational number. The thermal forces promote shape and orientation fluctuations around the steady configurations of the reciprocal non-Brownian chains. The competition between the reorientation mechanisms and the Brownian effects results in normal distributions of the orientation of the chains. In the stiff regime, these fluctuations cause the chains to fall faster than their reciprocal non-Brownian cases. With increasing flexibility, thermal fluctuations lead to more compact configurations of the chains and higher average settling velocity. Nonetheless, chain flexibility plays an important role on lateral migration. The interplay between elastic, gravitational, and thermal forces leads to important secondary influences on the filament settling dynamics.