How should a person suffering from flatulence perform tawaaf?

If the person is a ma`zoor then he may continue with the tawaaf within that salaah time even if he passes wind. A ma`zoor is that person who experiences a breaker of wudhu, like passing of wind or urine incontinence etc. so frequently that from the beginning of the namaaz time until the end of the namaaz time he / she is unable to perform wudhu and read namaaz without that particular breaker of wudhu occurring. Once this is established, one will remain a ma`zoor for as long as that particular breaker of wudhu occurs at least once in the rest of the salaah times that follow. If the person does not qualify as a ma`zoor then he will have to make wudhu whenever his wudhu breaks.

And Allah Ta'ala (الله تعالى) knows best.