Wong-Staal was born on August 27, 1946, in Guangzhou, Guangdong, Republic of China. She was born into a family of five, with two brothers and a sister. The Communist Revolution during the 1940s resulted in Flossie's family being one of many Chinese citizens who fled to Hong Kong in 1952. There, she attended Maryknoll Convent School, showing great potential in science. In 1964, Flossie pursued a Bachelor of Science degree in bacteriology at the University of California, Los Angeles, graduating as cum laude. She would later earn her P.h.D. in molecular biology in the same university. She would also continue her research at the University of California, San Diego. While pursuing her P.h.D., she married oncologist Stephen P. Staal in 1971. She would have two daughters before divorcing Staal around 1990. Before then, she would work with biomedical researcher Robert C. Gallo in the Laboratory of Tumor Cell Biology for her postdoctoral at the National Cancer Institute of the National Institutes of Health. She would later become the Florence Seeley Riford Chair in AIDs research at the University of California, San Diego, in 1990. Later on, she married neurologist Jeffrey McKelvy and would found Immusol, now known as iTherX Pharmaceuticals, together. On July 8, 2020, Wong-Staal would pass away at the Jacobs Medical Center in La Jolla due to pneumonia complications.

Wong-Staal's research focused on studying the molecular virology of HTLV-1 through examination of its transcriptional activators and posttranstitional regulators. With her team, they conducted research on human retrovirus Human T Cell Leukemia virus, determining it was causative agent in human adult T cell leukemia. Her postdoctoral work continued until 1973 where she researched retroviruses, which is a type of RNA virus that invaded the cellular nucleus where they would insert their genes into the host's DNA, and became the first researcher to clone HIV. She also helped in developing blood test for HIV through completion of genetic mapping of the virus. At the Center for AIDS Research in 1990, her research  would focus on gene therapy, which is used to treat or stop a disease by altering the genes inside the body, by using a ribozyme to repress the HIV in the stem cells.