Green’s Dictionary of Slang

boke n.2

also boak
[synon. Scot.; ult. OE bealcan, to belch, ‘throw up’]

(Ulster) vomit.

[UK]B. MacLaverty ‘A Happy Birthday’ in Secrets 30: Sammy belched and the operator dived to one side. As Sammy staggered away, the operator said to his mate, ‘There’s not a spot of boke on him’ .
[Ire]J. Morrow Confessions of Proinsias O’Toole 82: Other grisly details of the event, too boke-making to relate here.
[US]Eble Campus Sl. Fall.
[UK]N. Griffiths Grits 129: Roger thur, noddin out in the cornurr wuth ’is jeans caked in boak.
[Scot]I. Welsh Dead Man’s Trousers [21]: I feel boak rise inside me and fight it back down into my acrid guts.

In phrases

give one the boke (v.) (also give one the boak)

to make one sick.

H.C. Rae Skinner 13: ‘Booth always did give me the boke,’ Skinner says.
T. Varady New Writing and Writers 102: ‘It would,’ he told the earnest Langholm, ‘give me the boke.’.
‘my face your’ ‘Tasteless Toothpaste’ 13 Feb. halfbakery.com 🌐 I had some of this as part of a ‘complementary’ in-flight wash kit on Cathay Pacific in the 80s. It gave me the boak.
[UK]J. Fagan Panopticon (2013) 7: You’re giving me the boak, fuck-pus.
[Scot]A. Parks May God Forgive 127: ‘Smell of this place is giving me the boak’.