There almost was a Duke of Arkansas. Scottish financier John Law got close to French Royalty back in 1721 after cooking up a scheme to get that nation out of debt. His apparent success gained him a charter to manage the Louisiana Territory for 25 years. He set aside a 12-square mile concession for himself along the Arkansas River about 25 miles from where it meets the Mississippi.
Law’s financing, however, was based on promises that could not be fulfilled and his dream collapsed. If he had succeeded though, his concession would have been a duchy and he would have been Duke of Arkansas.