A seal assembly, for example, a face seal assembly for a machine such as a turbomachine, and an associated method of operating the seal assembly in the machine are disclosed. The seal assembly includes a rotatable seal component, a non-rotatable seal component, and a plurality of pairs of flexures. The non-rotatable seal component is disposed facing the rotatable seal component. The plurality of pairs of flexures is spaced apart from each other along a circumferential direction of the seal assembly. Each pair of the plurality of pairs of flexures includes a first flexure and a second flexure disposed in a stressed condition such that a portion of the first flexure and a portion of the second flexure are in contact with each other. Further, an end of the first flexure and an end of the second flexure are coupled to each other and to the non-rotatable seal component.