The same thing anyone would do with their lover...chuckle a little and continue on. Have you ever released trapped air from your vagina during sex (queef)? It's the same thing. "Eating dirty" is not unheard of, but usually the bottom will "clean" and "prep" for their lover if sex is planned. If sex is spontaneous, "rimming" or licking and tonguing the anal area may be replaced by fingering with saliva or lubricant. Those who engage in anal sex can't be faint of heart over things like flatulence or feces.
Lol! I was junking that's way less embarrassing while ur partner has his mouth down there...
Thinking*
When I saw this http://www.mangago.zone/read-manga/xi/mf/v01/c006/13/ and he said this is more embarrassing than farting all I could think was "What would actually happen if a guy farted while his partner was licking his a**hole?"