Green’s Dictionary of Slang

hum v.4

[abbr. hummer n.8 ]

to give fellatio.

[US]B. Rodgers Queens’ Vernacular 33: to suck a penis [...] hum a tune [on the flute] (’30s).
[Aus]B. Moore Lex. of Cadet Lang. 191: hum1 to peform fellatio (especially when the agent is a woman).

In compounds

hum job (n.) [job n.2 (2)]

(US) fellatio, which is intensified by the fellator humming as he/she sucks.

[US] in E. Cray Erotic Muse (1992) 254: My true love gave to me / A hum job in a pear tree.
[US]B. Rodgers Queens’ Vernacular 34: hum job (mid ’60s) an act where the sucker hums to heighten pleasure since humming gently vibrates the head.
[US]C. Hiaasen Double Whammy (1990) 208: ‘Two hundred bucks?’ ‘And a hum job if you want it, Father.’.
[Aus]B. Moore Lex. of Cadet Lang. 191: usage: ‘She gave me a great hum job last night.’.