An assembly for an aircraft includes a first shaft, a second shaft and a metering device. The metering device includes a device sidewall, a device first end, a device second end, a device bore, a plurality of channels and a plurality of ports. The device sidewall circumscribes the first shaft at the device first end. The device sidewall is disposed in a second shaft bore of the second shaft at the device second end. The device bore extends axially along the axis through the metering device between the device first end and the device second end. The channels are arranged circumferentially about the axis. Each of the channels projects radially into the device sidewall from the device bore and axially into the device sidewall from the device second end. The ports are arranged circumferentially about the axis. Each of the ports projects radially through the device sidewall.