Green’s Dictionary of Slang

shoot-flying n.

[? shoot off v. (1) + SE fly]

(UK Und.) the robbery of watches, wallets and similar small personal items.

[US](con. 1910s) D. Mackenzie Hell’s Kitchen 117: ‘Shoot-flying’ is the term used to describe the snatching of handbags and small parcels.
[UK]Thieves Slang ms list from District Police Training Centre, Ryton-on-Dunsmore, Warwicks 9: Shoot-flying: Bag snatching.
[UK]P. Hoskins No Hiding Place! 192/1: Shoeflying [sic]. Bag-snatching.
[UK](con. c.1900) A. Harding in Samuel East End Und. 75: In the early years he used to go what they called ‘shoot-flying’ – stealing watch chains by getting hold of them and tugging. They would go into a street with a lot of turnings and when they’d made their catch they would shoot down the turnings – that’s why they called it ‘shoot-flying’.
[UK](con. 1932) W. Woodruff Beyond Nab End 29: The old man and two of his older sons had done time for what Ben called ‘dippin’ or ‘shoot-flyin’.