'Faffing about' is a phrase that is most often heard in the UK rather than in other parts of the English-speaking world. In fact, even in the UK it is something of an anachronism, more at home in a P G Wodehouse story than as 21st century street slang.
'Faff' has been used to mean 'dither; fuss; flap' since the 19th century. The Church of England clergyman, author, and folksong collector Sabine Baring-Gould recorded it in Yorkshire Oddities, 1874:
T' clock-maker fizzled an' faff'd aboot her, but nivver did her a farthing's worth o' good.
'Faff' derives directly from 'faffle' which had been used since the 16th century, which much the same meaning but with the additional meaning of 'flap idly in the breeze'. The second meaning seems to be the source of another 1870s usage of 'faff', from The Australian Journal, 1879:
"No, it [a candle] burns quite steadily now; you are right about it faffing about before, because it blew towards my face."
Baring-Gould's citation locates the phrase amongst the rural working classes and its use in Australia at a time when English speakers in that country were predominantly ex-UK convicts, suggests that the phrase was to be found below rather than above stairs.