In 1880, Platt was taught etching by his friend and fellow artist, Stephen Parrish in Gloucester, Massachusetts. Platt often depicted this area in his etchings and from 1880 to 1890 he created over one hundred etchings.
As an architect, he began working in 1916 through the patronage of William Astor. Platt designed the Freer Gallery in Washington D.C. when in 1913, Charles Lang Freer asked him to design a new museum for his collection of American and Asian Art. The Freer Gallery was a "single-story building with a rusticated facade in the style of an Italian mannerist building. The interior was designed with a central courtyard enclosed by interior corridors and gallery spaces." Delayed by World War I the museum opened to the public on May 2, 1923.
In addition, Platt designed the Lyme Art Association in Old Lyme, CT and the Lyman Allyn Art Museum building in New London, CT. Platt was a part of the Old Lyme Art Colony in Connecticut.
During his career Platt received many awards, including the bronze medal from the Paris Exposition of 1900. He was a full member of the Society of American Artists (1888), the National Academy of Design (Associate, 1897: Academician, 1911), the American Academy of Arts and Letters, the American Institute of Architects, the New York Etching Club and the London Society of Painter-Etchers.