Is the Fajr prayer valid if performed before the two rak'ahs (sunnah) of Fajr at their prescribed time and before sunrise, knowing that the reason for this is frequent flatulence, and is the prayer considered invalid, requiring its repetition?

The Sunnah for the Fajr prayer is to perform the Raghibah (supererogatory) prayer before the Fard (obligatory) prayer. If someone prays the Fard before the Nafl (supererogatory), their prayer is valid, but they have gone against the Sunnah, and they should make up the Sunnah prayer. It is advised to pray the Raghibah first, then the Fard, to attain the full reward. As for continuous flatulence, it falls under the ruling of سلس (incontinence), and one must perform ablution for each prayer after its time has entered, and whatever is released thereafter does not invalidate it.