Burns's early work concentrated on flutter problems; her main concern throughout her career was the measurement of the loads imposed on aircraft structures during flight. Other wartime tasks included the development of windscreen wipers for bombers and the double windscreen enclosing a supply of warm air to improve visibility.In the late 1940s Burns became the first flight-test observer (FTO) in the UK to use strain gauges in an aircraft in flight. She obtained her pilot's licence in 1948, taking a Royal Air Force Elementary Flying Training Course in a de Havilland Tiger Moth. Early post-war work included flying on European air routes in British European Airways Vickers Viking airliners, travelling to Iceland, Norway and Spain to carry out gust measurements. It was at the RAE that she met her husband, Denis, who gave her LBW while umpiring during a men-versus-women staff cricket match.

They married in 1947.During the intensive investigations into the disastrous crashes of the early de Havilland Comet jet airliners, Burns flew in Comets as an FTO during 1954 and became the only woman to fly in an unpressurised Comet at an altitude of more than 30,000ft. During these flights the scientists wore parachutes which opened automatically at 17,000ft, and if they forgot to deactivate them they would open in the airliner's cabin. The following year Burns was awarded the Queen's Commendation in recognition of her contribution.Further recognition came in the form of the Royal Aeronautical Society's R.P. Alston Medal in 1958, for her practical contributions to aircraft safety as a flight-test observer. This work had mainly entailed the in-flight measurement of loads and determination of their effect on aircraft fatigue life. By this time she had flown some 800 hours as an FTO.In 1963 Burns was awarded a second Queen's Commendation, this time for her flights in an English Electric Canberra in Libya and Tunisia during Operation Swifter, carrying out low- and high-level-gust research. The Royal Aeronautical Society awarded her its Silver Medal for Aeronautics in 1966, and in 1968, when she was working on clear-air turbulence, flying as an observer in several countries, she was presented with the Whitney Straight Award for her services to aeronautical research and flying.In her years at the RAE up to her retirement in 1976, by which time she had logged over 1,500 hours in the air, Anne Burns wrote a considerable number of internal reports, a number of which were reprinted in Reports and Memoranda by the Aeronautical Research Council.

She maintained that the work of women scientists should be acknowledged on merit, and not because it was the work of women.In 1954 Anne Burns took up gliding. On her first cross-country flight, made from Lasham, Hampshire, in an Eon Olympia glider on 5 June 1955, she attained 5,400ft and ended up at RAF Tern Hill, Shropshire. In four hours and 55 minutes she covered 134 miles, beating the British women's distance record by 50 miles. On 2 December 1956, flying a Slingsby Skylark 3b, Burns was bungee-launched by six men from a ridge on the top of Long Mynd, Shropshire, to set new women's British national and UK absolute altitude and gain-of-height records. In a flight lasting just under three hours she reached 11,890ft and gained 10,500ft. Again flying a Skylark 3, on 21 August 1957 she became the first woman to cross the Channel in a sailplane.