What is the ruling on the prayer of one who suffers from irregular and uncontrollable flatulence, which forces her to repeat ablution and prayer many times for each obligatory prayer, and takes a long time to prepare for prayer? Does she have to repeat the prayer if flatulence occurs, or should she pray in her state and not repeat it, and is it permissible for her to supplicate during prayer with this condition?

Since the situation is as you described, with no known time for the wind to stop, the ruling for your ablution is the same as that for a woman experiencing irregular bleeding (mustahadah). It suffices for you to perform ablution for each prayer after its time has begun. With this ablution, you may pray as many prayers as you wish until the time for that prayer expires. As for obsessive thoughts (waswasah), you must ignore them and not give in to them, so they do not intensify.