After serving in the US Navy, Phelps worked at chemical instrument company Cole-Parmer in Chicago, Illinois, but a year later, not liking the cold Chicago climate, she returned to Tennessee. In June 2009, Phelps joined Oak Ridge National Laboratory. She started as a technician and was later promoted to research associate and program manager. Phelps works in the Nuclear Science and Engineering Directorate as the project manager for the nickel-63 and selenium-75 industrial isotope programs. As a member of Oak Ridge's Nuclear Materials Processing Group, she is part of the research and development staff, working with "super heavy" transuranic isotopes that are produced mainly by nuclear transmutation. She is also a member of the Medical, Industrial and Research Isotopes Group, where she researches elements such as actinium, lanthanum, europium, and samarium.
Phelps was involved in the discovery of the second-heaviest known element, tennessine (element 117). She was part of a three-month process to purify 22 mg of berkelium-249, which was shipped to the Joint Institute for Nuclear Research and combined with calcium-48 in a fusion reaction to create tennessine. In IUPAC's crediting Oak Ridge laboratory collectively as principal co-discoverer of tennessine, it acknowledged 61 individuals at ORNL who had contributed to the project including members of operations staff, support personnel, and researchers such as Phelps. It recognized Phelps as the first African-American woman involved with the discovery of a chemical element.
When Oak Ridge National Laboratory held a gala to honor and celebrate the team that discovered tennessine, Phelps's name was left off the list, and when she showed up, she cried as she realized that she did not have a seat at the table with the other scientists. In addition, a plaque to commemorate the discovery was created to be hung up in perpetuity at the laboratory, and once again, it omitted her name. Phelps was told that her name had been cut off by mistake due to a line break in a spreadsheet. While the laboratory later claimed that the "error [was] quickly corrected", it was only after Phelps fought for several months to have her name included that the laboratory acquiesced.
Phelps has contributed to additional research efforts, including those of spectroscopic analysis and spectrophotometric valence state studies of plutonium-238 and neptunium-237 and 238 for the National Aeronautic and Space Administration (NASA).  Phelps has also studied electrodeposition with californium-252 for the Californium Rare Isotope Breeder Upgrade project.
Phelps is a member of the American Chemical Society.