Green’s Dictionary of Slang

burk v.1

[? rhy. sl. burk = SE shirk or f. SE burk, to smother, to ‘hush up’. Both are ult. f. burke, to strangle (named after the early 19C ‘resurrectionists’ or grave-robbers Burke and Hare; see burke v.)]

(orig. N.Z.) to avoid work.

[NZ]McGill Dict. of Kiwi Sl. 23/2: burk to avoid work, c.1880–1920; G.B. Lancaster in Sons o’ Men: ‘I’ll exchange ... but I won’t burk, see?’.
[NZ]McGill Reed Dict. of N.Z. Sl. [as cit. 1988].