A seal assembly for a gas turbine engine according to an example of the present disclosure includes, among other things, a first side plate, a second side plate and a backing plate that extend circumferentially about an assembly axis. A first brush seal and a second brush seal are positioned on opposite sides of the backing plate such that the first brush seal is between the first side plate and the backing plate and such that the second brush seal is between the second side plate and the backing plate. The first brush seal is dimensioned to establish a first sealing relationship with a first gas turbine engine component. The second brush seal is dimensioned to establish a second sealing relationship with a second gas turbine engine component. A method of assembly is also disclosed.