What is the ruling on the prayer of someone who performed ablution and prayed Fajr while feeling a slight discharge of wind before and after the Adhan, and this recurred during the Rak'ahs until he feared missing the prayer time, so he repeated the ablution and the prayer, with the very slight discharge of wind continuing?

The emission of gas invalidates ablution. Your prayer is valid if you do not find enough time to pray with complete purity before the time expires, and what exits from you during prayer does not harm you.

However, doubt about the emission of gas is not considered an invalidator of ablution unless one is certain of its emission, because certainty is not removed by doubt.