Is squid farting when they spray ink?

No. There is a special bladder in the squid (and octupii) which contains the ink and is released when the animal frightened.

"Farting" (I prefer the euphanism, 'Breaking wind' although the verb 'to fart' is actually in the Oxford English dictionary!) is a biological process caused by the release of methane and other gases when bacteria breaks down food. The gas cannot be absorbed by the gut and is passed through the intestine and passed from the anus.