I've never heard it, either, but it bears mentioning that we constantly advise learners NOT to use the Urban Dictionary as anything more than a potential source of humor because of wacko entries.
It is probably worth warning that queef does not refer to release of gas from the anus. To use it for such could lead to embarrassment.I've heard 'queefed' , but not beefed.
As for 'beef' meaning 'fart'. I've never heard of it.
I grew up in Northern California in the 80s & 90s and it was one of the most common descriptives for flatulence. I don’t think I hear it much now that I live on the East Coast.