Really burning anything is bad for the environment but cardboard although not good for the environment to be burned is not really toxic when burned unlike plastics, rubber etc that release toxins into the air.
I always throw a bit of cardboard into my outdoor fire pit to help get the logs going and never had a problem.
Just put little pieces of the cardboard into the fire pit at a time to avoid it flaking off too much if that's what you plan to do.
I would not however try burning cardboard in a fireplace because it could start a fire in your house due to it flaking apart and flying through the air but outside it's usually safe to burn the cardboard.