Flexures are components of micro-mechanisms efficiently replacing classical multi-part joints found at the macroscale. So far, flexures have been limited to two-dimensional planar designs due to the lack of a suitable three-dimensional micromanufacturing process. Here we demonstrate and characterize a high-strength transparent monolithic three-dimensional flexural component fabricated out of fused silica using non-ablative femtosecond laser processing combined with chemical etching. As an illustration of the potential use of this flexure, we propose a design of a Hoecken linkage entirely made with three-dimensional cross-spring pivot hinges.