What should someone do who suffers from continuous flatulence that stops at a certain time, and it is difficult for him to wait until the last moment for purification and prayer, knowing that the time for 'Isha prayer is late and the time for Fajr prayer is early where he resides?

If you find a time within the prayer period sufficient to perform it with proper purification, then you are not one of those afflicted with سلس (incontinence), and you must wait for that time to perform ablution and pray. If waiting is difficult for you, then sleep while taking measures to wake up. If you wake up at the appropriate time, perform ablution and pray. If you do not wake up, there is no sin upon you.