There are very strict guidelines to follow when transporting firearms and ammunition via air travel. The TSA has very clear guidelines on how to properly pack and present your firearms and ammunition when checking in for your flight.
In addition they also provide the following for transportation of big game meat:
Carry On Bags: Yes (Special Instructions)
Checked Bags: Yes
Meat, seafood and other non-liquid food items are permitted in both carry-on and checked bags. If the food is packed with ice or ice packs in a cooler or other container, the ice or ice packs must be completely frozen when brought through screening. If the ice or ice packs are partially melted and have any liquid at the bottom of the container, they will not be permitted. You also can pack frozen perishables in your carry-on or checked bags in dry ice. The FAA limits you to five pounds of dry ice that is properly packaged (the package is vented) and marked.