Walter Chew Flower was born in East Feliciana Parish in 1850, the son of a planter and cotton factor. Flower was educated at Pass Christian College and also studied law at the University of Louisiana (later Tulane University). After leaving school, he worked for several years as a reporter for the Daily Picayune and briefly practiced law before joining the cotton factoring firm of Edwin Nall & Co. In 1884, he founded his own firm, Flower Brothers, with his brother Ivy, and in 1888 formed a partnership with Branch M. King; in 1891 the firm became Flower, King and Putnam. He served as President of the New Orleans Cotton Exchange in 1891 and 1892 and retired from the business in 1895.

In 1896, Flower was chosen by the Citizens' League, a non-partisan reform group dedicated to overthrowing the current political regime in New Orleans, as its candidate for Mayor. Flower defeated the regular Democrat candidate Charles F. Buck.

The Flower administration brought in a municipally owned water, sewer, and drainage system and placed the port facilities under a publicly controlled board. It was during the Flower administration that the 1896 city charter was implemented, which cut the city council to 17 members, increased the mayor's appointive powers and (briefly) instituted a system of civil service. Flower also worked to de-politicize the Police Department and to combat epidemic disease. The City Council passed the infamous "Storyville" ordinance in 1897 during Story's time in office.

In 1900, the regular Democrats returned to power with the election of Mayor Paul Capedeville. Flower died of tuberculosis at his summer home in Covington later that year.