Her lawyer said she had made the decision to save herself, and the Air Force, further embarrassment.
The case had been due to open at Minot Air Base, North Dakota, tomorrow.
Ms Flinn, whose predicament has rarely been out of the headlines in the past week, became something of a star two years ago when she qualified as the first woman bomber pilot in the US Air Force.
At the end of last year, however, at the age of 26, she was grounded, pending court martial for a catalogue of crimes which included adultery.
If the case was embarrassing for Ms Flinn, whose chequered love-life was picked over by even the most upmarket American newspapers, it was doubly so for the military, as some of its top brass candidly admitted. Their star pupil was in disgrace; upwards of $1m of training had apparently gone to waste.
Now, only a few days after the Air Force denied a report that that it was discreetly suing for peace, a deal appears to have been done. If convicted as charged, Ms Flinn would have faced prison, a dishonourable discharge, and a ban on flying in military or civilian life. An honourable discharge would enable her to take a commercial pilot's job.
The Air Force stands to gain far more: it will avoid having its policies and practices subjected to long and contentious public scrutiny. For if one case exemplified the confused intersection of military discipline and sexual politics in the United States today, this was it.
Ms Flinn's version is briefly this. After Air Force Academy and bomber- training school, she realised her ambition to become a B-52 pilot. Stationed in the freezing, windswept wilds of North Dakota near the Canadian border, she was starved of company. She felt out of place at the officers' club and unwelcome at the wives' club, but she knew the rules.
Men junior or senior to her in her own command were off- limits. She declined to date colleagues of equal rank, regarding it as unprofessional. She had a brief fling with an officer in another command. But last year, she fell in love - innocently, she maintains, but unwisely - with a civilian sports coach who told her - falsely - that he was separated.
The relationship went wrong. She discovered his lie; he drank and turned violent. Ms Flinn's superior officer learnt of the affair and ordered her to end it. She obeyed, then disobeyed when her lover attempted suicide. Then she lied to cover up: a train of events in which one "mistake", as she calls it, triggered a succession of military crimes. Opinion in the civilian world was generally kind to Ms Flinn; but the military - and the Air Force in particular - was fiercely divided. Hardliners maintained that anyone who lies to a superior officer, whatever the circumstances, has no place flying bombers, serving in the Air Force, or in the US forces at all.
Others, however, regarded the court martial as absurd over-reaction, if not sexual discrimination. Ms Flinn, they said, did nothing that countless male officers had got away with, and nothing that some timely advice or at most a reprimand might not have solved. They pointed out that neither of Ms Flinn's admitted liaisons breached fraternisation rules, and that she became aware too late that the second affair was adulterous. This more charitable view, however, comes up against the unimpeachable fact that the law on adultery in the military was enacted not by the forces but by the US Congress. So, if the rules are to change, this is a matter for Congress.