What is the ruling on the prayer of one from whom wind continuously exits from the anus, resembling flatulence, and from the front, such that he performs ablution and repeats the prayer multiple times?

If you doubt the emission of wind, the default assumption is its absence, and your ritual purity (wudu') is not invalidated except by certain conviction. If wind is emitted from the anus and you are certain of its emission, and if it is continuous, not stopping for a period sufficient for purification and prayer, then your ruling is that of one afflicted with incontinence (sahib al-salas). You perform ablution for prayer after its time has begun, and you pray with this ablution as many obligatory and supererogatory prayers as you wish until that time exits. As for wind emitted from the front private part (qubul), it invalidates ablution according to the majority of scholars, and if its emission is continuous, its ruling is as previously mentioned regarding anal wind.