"The dry dust would get into his throat, causing an abnormal thirst and choking sensation which could only be allayed by copious amounts of beer, or by a few pence to purchase the needful stimulant."
"Flying dustman" is a Victorian misnomer. Such a job did not entail flying, but referred instead to the dustmen's habit of hurrying off from district to district. Nor did the occupation entail the collection of mere dust: the flying dustman collected all household refuse. The dustman, travelling by cart and horse, gathered up dust and refuse which he collected in his cart.
Flying dustmen had a monumental task. In 1877, the city of London contained about 20 parishes (http://mapco.net/parish/parish.htm). The parish of Lambeth alone, had 40,000 rateable houses. Each house produced an average of three loads of dust per year, making for one gigantic dust mound.
Foremen were supposed to make sure that the flying dustmen did their jobs, to prevent dust mounds on every corner. However, that wasn't always the case. In other cases, the flying dustmen did their jobs, but expected a tip.
"Under the old system, householders were constantly lodging complaints against the dustman who was seldom to be found when his services were needed. [He] had his own way of letting it be known that his services were not gratuitous. The dry dust would get into his throat, causing an abnormal thirst and choking sensation which could only be allayed by copious amounts of beer, or by a few pence to purchase the needful stimulant. This sort of blackmail is still levied, although the authorities of the parish are making the most strenuous efforts to have it abolished, having inscribed on each cart a caution against the bestowal of gratuities." (http://www.victorianlondon.org/professions/dustmen.htm)
Far from being useless, the dust had many purposes in Victorian London. "Not many years ago dust had a high value; it yielded the following among other marketable products: fine dust, used in making bricks and as manure; coarse dust or "breeze", used in burning bricks; rags, bones, fragments of tin and other metals, old boots and shoes, paper, etc." I suspect, however, that with time, the city's uses for dust started to wane as was the case with horse manure. What wasn't recycled was deposited into urban shoots or on to boats to be carried down the River Thames.
Flying dustmen courtesy http://www.victorianlondon.org/publications/thomson-34a.png.