Kennedy attended the local schools and Geneva College, then at Northwood, Ohio.
At the beginning of the Civil War Kennedy joined the first company from Logan County, Ohio, which started for camp at Columbus on the Tuesday succeeding the firing upon Fort Sumter. The company went into three months' service but later joined the 23rd Ohio--the first three years' regiment from the state. Entering the service as a second lieutenant, Kennedy served as assistant adjutant-general, being promoted captain on October 7, 1862, and major on November 16, 1864. He resigned on April 8, 1865, but was recommissioned six days later as colonel of the 196th Ohio Infantry. He had been brevetted on March 13, 1865, lieutenant colonel of volunteers for gallant and meritorious service during the campaign in West Virginia and in the Shenandoah Valley, and brigadier general of volunteers for distinguished gallantry during the war. He was mustered out of service on September 11, 1865. At the battle of Antietam in 1862, by the fortunes of war, he was in temporary command of a portion of the left wing of the army, and upon the review of that army by President Lincoln on the battlefield, he was called to the front and presented as "the youngest commander of the Army of the Potomac. "
After leaving the army Kennedy returned to Bellefontaine where he studied law and was admitted to the bar in 1866. He then entered a law partnership, West, Walker & Kennedy, and continued in the firm until 1878. In that year he was appointed collector of internal revenue for the fourth district of Ohio by President Hayes and served until 1883. Two years later he was a candidate for governor on the Republican ticket but was defeated for the nomination by Joseph B. Foraker. The convention then by acclamation nominated him for lieutenant-governor. He was elected and while serving in that capacity acquired by reason of his sturdy rulings the appellation of "King Bob. " He resigned his office on March 3, 1887, having been elected to the United States House of Representatives in the fall of 1886. He served in the Fiftieth and Fifty-First congresses (March 4, 1887 - March 3, 1891) but was not a candidate for renomination in 1890.
In 1899, following the Spanish-American War, he was appointed by President William McKinley a member of the Insular Commission to visit Cuba and Puerto Rico to investigate and report upon conditions existing in these countries and to formulate a code of laws for Puerto Rico. He became president of the commission. After the Civil War he was active in every presidential campaign in nearly every state from Maine to Kansas. In 1903 he published Historical Review of Logan County, Ohio. He spent practically all of his life in his native city of Bellefontaine, Ohio, but died in Columbus, Ohio.
Kennedy was a member of the Presbyterian Church.
Kennedy was a member of the Republican Party.
Kennedy was a member of Scottish Rite Freemason.
On December 29, 1862, Kennedy was married to Mary Lewis Gardner of Bellefontaine. After her death he was married, on September 4, 1894, to Emma (Cowgill) Mendenhall of Wabash, Indiana.