Does prayer become invalid if one involuntarily passes wind, given that he constantly suffers from flatulence? Is this considered سلس الريح (incontinence of wind)? And what is your guidance for someone who, because of this, repeats his prayer at home after completing it in the mosque?

If flatulence is continuous to the extent that you cannot find enough time to pray with proper purification, or if the time it stops is irregular, then you are afflicted with سلس (urinary or fecal incontinence, or chronic discharge). In this case, you must perform ablution for each prayer after its time has begun, and the prayer will not be invalidated by the emission of flatulence.