Green’s Dictionary of Slang

(UK Und.) a bout of hedonistic enjoyment; a brief act of intercourse.

1773		Harris’s List of Covent-Garden Ladies 94: This lady [...] will not therefore grant a flying favour under two pounds two.
1865		Leaves from Diary of Celebrated Burglar 18/1: When Polly Nick heard of her ‘bloke’ going to Brighton with ‘Scotch Johnny,’ she made up her mind to have a ‘flying’ in Manchester.