What should one do who hears a sound resembling that of passing wind during prayer, cannot discern its source, and doubts the invalidation of their ablution or the defilement of their outer garments, especially considering they suffer from frequent flatulence?

If you are not certain that a wind has exited, then your ablution is not invalidated, for the fundamental principle is the continuity of purity, and certainty is not removed by doubt. If the emission of gases is continuous throughout the time, such that you do not find sufficient time for purity and prayer, then perform ablution and pray, and what exits from you will not harm you. As for doubt concerning the transfer of impurity to clothing, it should not be given attention, because the transfer of impurity is not established merely by doubt.