Yes, they did gain monetary benefit from their invention. The most obvious source is the Wright Company, founded on the 22 November 1909 by the Wright Brothers and with several prominent industrialists from New York and Detroit. Initially Wilbur and Orville received $100,000 and a third of the shares of stock. (Alongside this money they would have received gain from sales from this company, and royalties from others copying their patent.)

It's also interesting to note that in an interview in 1939, Orville said "If we had been interested in invention with the idea of profit, we most assuredly would have tried something in which the chances for success were brighter. You see, we did not expect in the beginning to go beyond gliding." (Harpers Magazine, “How the Wright Brothers Began,” Fred C. Kelly, October 1939.)