sip, noisy, quack
呷 centers on taking in liquid in small amounts (sipping) and on producing abrupt, noisy sounds like quacking. The meanings are loosely connected through the idea of a mouth making short, repeated actions.
呷 combines 口 (mouth) with 甲, which likely contributes the sound. The exact historical development is uncertain, but the structure suggests a phono-semantic compound where 口 indicates the action is related to the mouth.
The mouth 口 beside 甲 (which resembles a helmet or shell) suggests a mouth making small, sharp sounds or taking tiny sips, like a duck quacking or sipping water.
For コウ, imagine a duck sipping water and then letting out a loud 'ko' sound: 'ko' -> コウ, repeated as it quacks and sips.
to gulp down (alcohol, poison, etc.); to quaff; to down