"[焚]{た}く" means to burn, make a fire, like kindle firewood and coal. "[炊]{た}く" means to boil, like boil water in the boiler, or cook, like cook rice.
Actually you cannot burn insecticides such as being sold by the name of Barusan - a rat mite-cite. But when you add water to Barusan up to the designated line inside the container, it erupts white gas like a smoke screen as if something burning.
“いられなくなって” means “I cannot stay there.” If you set up Barusan in your living room or bedroom and once it starts to smolder, you got to rush out of the room, otherwise you’ll be choked.
Please note that "[焚]{た}く"and "炊{た}く" are different words, though phonetically sound the same.