I heat my house with Gas and cook on a gas stove. I have had birds in this house for going on 3 years. They are fine. But, if your pilot light burns out and you have a gas leak I would imagine this would harm your bird.
Whenever I cook my birds are no where near the kitchen. Overheating a cooking oil on accident can cause respitory problems.
My stove has an auto-ignition switch (which means it doesn't ahve a pilot light that stays lit.) So when I turn it on it turns on the gas and lights it for me.