Breckenridge began drawing at an early age. He commenced his formal art education at Philadelphia's Pennsylvania Academy of the Fine Arts in 1887. With a scholarship awarded him by the Pennsylvania Academy in 1892, and in company with Walter Elmer Schofield, he went to Paris. There he studied under Gustave Bouguereau, Lucien Doucet and Gabriel Ferrier, after which time he executed portraits and impressionistic landscapes.
Breckenridge joined the faculty of the Pennsylvania Academy of the Fine Arts in 1894, an affiliation that he maintained throughout his life; in 1934, he was appointed Dean of Instructors.
In 1909, the artist traveled to Europe, again with Schofield, visiting Belgium, England, France, Italy and the Netherlands. It was at this time that he studied the color theories of Michel Chevreul, which influenced his own advanced color technique. Although he had supported himself as a portraitist from 1905 to 1915, Breckenridge worked in styles ranging from realistic portraiture and Impressionistic landscapes to pure abstraction. By 1917 he was associated with the "Thirty-One," a group of Philadelphia modernists which included Charles Demuth, Charles Sheeler and Arthur B. Carles.
Breckenridge was a noted teacher; Edward Redfield and Daniel Garber were among his students. With Thomas Anshutz he established the Darby Summer School of Painting in Darby, Pennsylvania in 1898. When the School moved to Fort Washington two years later, Breckenridge purchased a house there, which he named "Phloxdale." He also founded the Breckenridge Summer School of Art in Gloucester, Massachusetts, in the mid-1920s, by which time his subject interest had turned largely to still life and his style to abstraction.
By the time of Breckenridge's death he was among the most well established and honored painters in the art world of Philadelphia. Although he exhibited consistently in Academy shows from 1898 until 1931, his strong identification with Philadelphia and responsibilities to the Pennsylvania Academy, may have mitagated against his being made a full Academician.