Is my current situation—in which I suffer from frequent and sudden intermittent flatulence during prayer, to the extent that I hear its sound and fear my prayer might be invalidated—considered a case of " سلس الريح" (incontinence of gas), which would permit me to apply its rulings to relieve myself of the obsessive thoughts and anxiety I am experiencing?

One who has performed ablution (Wudu') is not judged to have invalidated it merely by doubt, and certainty is not removed except by certainty. What the questioner has mentioned indicates that she is afflicted with waswasah (obsessive whispering), for the mawsoos (one afflicted by waswasah) may come to regard delusions as realities. If the questioner is certain, with a certainty beyond any doubt, that wind has been expelled, and the wind is expelled continuously such that she does not find a time to pray with a valid state of purity, or if the time of its cessation is not regular, then she is afflicted with sals al-reeh (continuous flatulence) and the rulings pertaining to a person with continuous discharge apply to her.