She was educated at the Polytechnic School, and then did her undergraduate studies at the University of California, Los Angeles, graduating with a bachelor's degree in 1969.

She joined the pioneering bone marrow transplant team in 1973, under E. Donnall Thomas, and became founding Director of Clinical Statistics at the Fred Hutchinson Cancer Research Center in 1975.

At that time, patient records were stored on punched cards, and Flournoy writes of sorting data sets manually at the laundromat while doing laundry.

[1] Her dissertation, supervised by Lloyd Delbert Fisher Jr., was The Failure-Censoring Bichain and the Relative Efficiency of Selected Partial Likelihoods in the Presence of Coprocesses.

To push this area forward, she organized a special session on the topic in 1989 (where she met her frequent early collaborator Steve Durham) and an entire conference on it in 1992.

[1] In 2000 the Committee of Presidents of Statistical Societies gave Flournoy their Elizabeth L. Scott Award "for her innovative and highly successful efforts in encouraging women to seek competitive research funding; for envisioning and supporting the pioneering Pathways to the Future Workshops; for serving as a role model and mentor for graduate students and young faculty; for her scholarship in teaching and research, and for her many contributions to the statistical sciences".

[5] In 2007 they gave her their Florence Nightingale David Award "for her fundamental research contributions in adaptive designs, sequential analysis, clinical trials, and particularly in bone marrow transplantation trials; for her devoted teaching; for her passionate mentoring to young statisticians, new investigators, women, and minorities, and researchers in small universities; for her leadership in the profession including her role as the chair of a major statistics department".