Phelps struggled academically in college. Unable to find employment after graduating, she joined the United States Navy. Phelps enrolled in the Navy's Nuclear Power School, which she credits with teaching her "how to study". Phelps studied nuclear power, reactor theory, and thermodynamics, and graduated in the top 10% of her class of 300–400 students. In 2019, Phelps told an interviewer that she pursued nuclear chemistry in part because of the lack of black women in the field, commenting: "They needed to see somebody like me sitting in the same spaces that they were at, and excelling in that same space."
Phelps served as a non-commissioned officer in the United States Navy Nuclear Power Program. She spent four and a half years aboard the aircraft carrier , operating the nuclear reactor and steam generator chemistry controls, and maintaining the water in the reactor. She was deployed twice, and was the only black woman in her division on the ship.