Your teflon coated non stick cookware is toxic to all birds. Anything else will be fine - cast iron etc. Also watch any scented sprays, plug-ins, scented candles even, or aerosol spays anywhere near them. They are also toxic to birds. One lady lost many expensive (and much loved) macaw parrots because of the product she cleaned her oven with.
Did they happen to say why? I'd love to hear that reason. Do you have any idea how many people brood chicks in their house and never have any problems at all with cooking?
It is possible to poison your chicks, but there is a thing caused dosage. If you have a teflon coated bulb in your brooder and that brooder has really poor ventilation it could be a problem. But the amount of teflon gas from a cooking pan in the kitchen that will make its way into the brooder I don't think so.
Most chick poisoning comes from tainted food or water or using cleaning materials in the brooder without airing it out well. Chickens do have a fairly delicate respiratory system so watch stuff used in their vicinity. But general cooking in the kitchen would not cause me any worries whatsoever.