Between the 1870 and 1880 census records, he moved to Texas with his older sister. He worked as a buffalo hunter and taught school. J.G. Kenan and Company bought the drug company of Ryus & Kumpe, in the drug and medicine business in 1881 at Fort Griffin, Texas. Mr. Kenan moved to Fort Griffin in the spring of 1880 and quickly proved himself to be an honorable gentleman. In 1882, J.G. Kenan moved to Seymour, Texas from Fort Griffin and his brother, D.L. Kenan, came out from Florida. J.G. Kenan became a Master Mason in 1889 at the Seymour Lodge and was selected as Worshipful Master that same year. In 1882, J.G. Kenan was the founder of the Baylor Drug Store at Seymour which was the first drug store. For the first years of its existence, the location was in the Clough building. In 1929, the drug store was in the Hawkins building where it was located in 1908. He sold the store years later to H.D. Hockersmith. In 1890, J.G. Kenan was among seven other men who organized the First National Bank at Seymour. The first city election was held in 1890, and J.G. Kenan was elected alderman. In the first city council meeting, J. G. Kenan served as secretary pro-tem, until L.A. Donnell was duly elected to the position. J.G. Kenan was elected the Seventh Baylor County, Texas Judge in 1893, and served two terms until 1897. He did not run for re-election. J.G. Kenan ran a drug store for many years in Graham and Seymour, Texas. He sold blank books and stationery, school and music books, paints, oils and wallpaper, jewelry, clocks and watches, furniture, coffins, undertaking supplies, and domestic sewing machines. He sold his drug store in Seymour to H.D. Hockersmith. He moved to Seymour from Fort Griffin in 1882. He was made the Worshipful Master Mason of the Seymour Lodge in 1889.

Jesse Gregory Kenan married Mary Lillie Cummins. Two children were born to this union: Nil Kenan and Dan Cummins Kenan.

He spent most of his adult life at El Paso, Texas. After the death of his son-in-law, Jesse Kenan moved to Okmulgee, Oklahoma to live with his daughter, Mrs. Nils Gill of Muskogee, Oklahoma and help her raise her four sons. He was active in community affairs. Jesse Kenan was a member of the Methodist church and organized the Men's Bible Class. He walked extensively and rode a bicycle until the age of 89 according to the newspapers. He was a man of integrity and character.