If you were an Officer during the early war years, VERY feasible (progressively becoming less feasible over time, but not impossible).

Firstly, lets talk about manning. During the war the Corps underwent enormous expansion - from four squadrons of about 24 planes each (with a fifth squadron as a depot unit) in 1914; to 450 planes being available in 1916 supporting the Somme offensive; to 1918 when 1000 aircraft could be lost during the Spring Offensive with aircraft reserves enough to seize back Air Superiority during the 100 Days. And all this while the life expectancy of the typical pilot was not high (roughly two weeks, but varying depending on what period of the war the pilot served through). Finding and training enough suitable Officers for this insatiable machine was a daunting task - especially during the first few years, when the pipeline from enlistment to squadron was not as efficient as it would be during the later war years. Young officers from regiments sidelined by the nature of the fighting were encouraged to, could, and did transfer to the RFC, returning to England to go through pilot training.

Complicating manning, and encouraging the use of "pre-existing" officers was that in the RFC being a pilot inherently meant being an Officer, and the culture that built up around that made switching to NCO flyers impossible. (The RFC allowed observers to be NCOs, and these men often "made the leap" to Officer by volunteering for pilot training after proving themselves in the squadron.) Why this state of affairs? Culture. The RFC had started operations almost as a private club, made up of men with the time and inclination to learn to fly privately. The relationship between pilots and ground-crew almost mimicked the young lord with a motorcar and his garage mechanics. This meant that the Corps was selective with its pool of applicants, seeking pilot material from out of the gentlemen/gentry/yeoman class. Complicating this was the best pilots requiring a moderately high level of education, and some sort of technical background. Early planes were inherently difficult and dangerous to fly, and required some familiarity with all the latest modern technology, like ICEs, the ability to do maths on the fly, and the ability to quickly adapt to changes in technology and warfare. So a common infantryman would be unlikely to be accepted into pilot training for cultural and educational reasons, but an infantry Officer who used to tinker with cars would likely be accepted. Does that make sense?

Officers from cavalry and artillery backgrounds were especially likely to be accepted. Cavalry because of the traditional scouting/reconnaissance roles that formed the RFC's first primary duty; artillery because of the technical nature of those officers, and the fact the second most important RFC job was to range and direct artillery batteries onto targets. Familiarity with especially how batteries operated, battlefield uses of new wireless sets, and the principals of discovery and navigation, were huge bonuses when training pilots for these tasks.

As the war went on, the training of pilots became more steamlined. The RFC was attractive to the best kinds of young recruits, and lessons from the air war grew more distinct from the lessons one could learn from the war on the ground. The culture of the RFC grew more distinct from the Army they served. Finally, the junior Officer corps of 1914/15 got promoted or killed, to be replaced with a new cohort who had received the opportunity to enlist in the RFC directly. There were still some transfers, but the rate decreased.

There are several memoirs about early flying with the Corps which elaborate on what I say briefly here; "No Empty Chairs" is a good entry-level popular book to read, and lists most published primary material of this type in its appendix.

/u/elos_ may be a good person to answer this, but let me share with you the story of Arthur Whitehouse, who was 18 years old when the war began in 1914. Whitehouse had come to the United States at age 9 and worked at the Edison Storage Battery Company as he grew older.

Whitehouse resigned from that job and boarded a ship back to England, joining the Northamptonshire Imperial Yeomanry. He trained as a member of a machine gun crew and served at the front until in 1915 he requested and received a transfer to the Royal Flying Corps. Trained machine gunners were in demand, due to casualty rates, and Whitehouse was accepted an airfield and put into a plane straightaway as a rear-seat gunner.

He earned the Military Medal and logged hundreds of hours in the air as a gunner. After volunteering several times for pilot training, he was transferred to England in January 1918 to become a pilot. He had his solo flight on June 14, 1918 and became a commissioned officer after being certified as a pilot.

He flew several coastal defense missions patrolling for German bombers but was never deployed back to France. In late 1918, he (and many other British soldiers with more than 3 years service) was granted 10 weeks' leave. He chose to return to New Jersey and his family, and he was there when the war ended.

While he never shot down another plane while serving as a pilot, he shot down several as a gunner and recorded more than 1,300 hours in the air as a rear-seater.