Green’s Dictionary of Slang

barking spider n.

[the resemblance + the noise of defecation or farting; ult. the Aus. barking spider, which produces a barking or whistling noise]

1. (US campus) the audible breaking of wind.

[US]P. Munro Sl. U.
Dly Record (Morristown, NJ) 23 Nov. A15/2: Some euphemisms for passing gas [...] Air biscuit, backfire, bark, barking spider [etc].
OnLine Dict. of Playground Sl. 🌐 barking spider n. something to blame when breaking wind loudly.

2. the anus.

[UK]Roger’s Profanisaurus in Viz 87 Dec. n.p.: barking spider n. Ringpiece; anus; chocolate starfish (qv).
[UK]M. Manning Get Your Cock Out 7: How he had managed to get that purple monster up her barking spider was anyone’s guess.