He began working as a draftsman in various architectural offices in San Antonio by the time he was twenty.
He briefly served in the Spanish–American War.
From 1902 to 1909 Phelps opened several architectural firms both by himself and partnering with others.
He firmly established himself in a solo practice between 1910 and 1940.Phelps designed buildings in several architectural styles such as Romanesque Revival, Mission Revival, Beaus-Arts and Streamline Moderne.
Phelps married Laura Clamp in San Antonio in 1905 and the couple had two children.