alt Hacker News> "kai" (pronounced ke like in keg)
Ancient Greek spans several centuries of sound shifts and many dialects. It cannot easily be simplified into one specific pronunciation, particularly not one that is based on your specific dialect of English. Wiktionary has /kǎi̯/, /ˈkɛ/, /ˈcɛ/ and /ˈce/ for "καὶ".
You don't have to span several centuries to witness that. "και" is pronounced in several different ways in modern greek as well. But that's besides my original point.