Chamomile reached English through Latin from Greek, where its name meant earth apple. In words that come from Greek, ch usually stands for a k sound: chaos, character, chemistry and chameleon all start with k.
English kept the Greek-style ch in the spelling. British English also spells the word camomile, without the h, and says it the same way.
The last syllable is the word mile in both accents, and Cambridge also lists KAM-uh-meel for American English. Whichever ending you choose, keep the stress on KAM and the middle syllable short: uh.