I do not have any record of a William Fluckey born in 1833.That is not to say there was not one, but I cannot find any record of him.
However, regarding George Fluckey and Elizabeth Bennett, parents of William C. Fluckey, George was the son of John and Mary Johnston Fluckey.He was born between 1817-1818 in Cardington, Morrow Co, OH, and he died 1879 in South Bend Co, IN.He married Elizabeth Bennett April 20 1837 in Marion Co, OH.She was born 1818 in (I think) Jefferson Co, OH, daughter of Leoffert Bennett and Magdalene Hardenbrook.
They had six children:Sarah J. b. 1838; Stephen B. b. abt 1841; William C. b. abt 1843; Malinda A. b. abt 1845; James A. b. abt 1847; and Mallissa E. b. abt 1849.
William C. died Aug 13 1864 in Knoxville, TX.During the Civil War, on May 7, 1864 he enlisted in the Union Army as a Privatein I Co 128th Inf Reg, IN.He died at Knoxville, TN on 13 Aug 1864.(Source:Report of the Adjutant General of the State of Indiana, INRoster, published by Holloway on 1865-66.)