Agricultural operations are currently exempt from air quality regulations on the premises of the farm operation unless the federal Environmental Protection Agency (EPA) says otherwise. Local municipalities have authority to regulate air quality. Check your local ordinance before incineration.
Incineration is not the same as open air burning. Open air burning is not a legal way of dead stock disposal.
Incineration requires a special unit specifically designed for that purpose. The best incinerators have the burner above the animal(s) or are fitted with a flue after-burner to eliminate smoke.