How to remove mildew smell frim leather coat

Leather can be in many forms. It's difficult to distinguish sometimes real from a man made product. However for real leather A coat might be called a finished leather ( shiny ) or a suede finish. If it's shiny you would wipe it down with a Damp cotton cloth. That will clean it off, no chemicals of any kind. It's the skin of a cow and will take on the odor of things that come in contact with it and smoke. Airing it out it will help but might require a good dry cleaner that specializes in leather.
If it's suede brushing it is about all you can do on your own. The lining of a coat is usually smooth satin or a polyester. That also could be wiped down with clean damp cloth also. No soap it will go thought the lining and wet the leather.