I can find no published study or even an oblique reference to the myth that suggests they might not! Seagulls, and birds in general, have a single opening called the cloaca, which serves for removing both the waste products of the kidneys and the intestines. This has a muscular sphincter to hold it closed, much like the anus. The bird’s digestive tract, though shorter than ours, still contains bacteria and these bacteria will produce gas. When the gas pressure exceeds the elastic strength of the cloaca sphincter, the result must inevitably be a fart. Possibly the reason seagulls might have acquired a reputation for never farting is that when a seagull poops in mid-air the person below suffers the immediate consequences. But with a mid-air fart, who’s to know?