"Reality" show stars typically don't make a lot per episode. The fact that labeling a show "reality" permits them to film and feature shows with non-actors (therefore ppl not protected by SAG, the actors guild) whom get paid a small portion of what a SAG actor would be paid. For the ppl on Duck Dynasty the $$ is made in free advertisement for their products, and royalties from show based items sold by the network like T-Shirts, hats, etc. Doing the show makes money as opposed to paying for a fraction of the advertising exposure the show gives them. If I were to make a guess I'd say no more then $4k-$5k TOPS.
To know how much money the cast of "Duck Dynasty" makes per episode then it's good to contact their customer service. They will be in a better position to give you a rough estimate of the amount got. You can also log in to the official website so as to get any updates.