My factory installed dryer vent does not have a spring loaded flapper - it is free to "swing in the breeze"
That being said, I have never heard it flap in the wind. It maybe the way you are parked and the wind is getting underneath the flapper. Or is the trailer level to allow the flapper to be closed when the dryer is not running?
Are you sure it is the flapper on the dryer vent? I have had other noises like slide topper awnings or main awning move around at night and wake me up, or something outside banging against the trailer. Sorry, don't mean to be patronizing, but I have been fooled about "what's that noise" in the past myself.
Brian